The 22nd International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
August 8–August 11, 2014 Dongguk University Gyeongju, Republic of Korea The 22nd International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
http://22.icfidcaa.org
August 8–11, 2014
Dongguk University
Gyeongju, Republic of Korea
Organized by
• Dongguk University (Gyeongju Campus) • Youngnam Mathematical Society • BK21PLUS Center for Math Research and Education at PNU • Gyeongsang National University
Supported by
• KOFST (The Korean Federation of Science and Technology Societies)
August 2, 2014 Contents
Preface, Welcome and Acknowledgements ...... 1
Committee ...... 3
Topics of Conference ...... 4
History and Publications ...... 5
Welcome Address ...... 8
Outline of Activities ...... 9
Details of Activities ...... 12
Abstracts of Talks ...... 30 1 Preface, Welcome and Acknowledgements
The 22nd International Conference on Finite or Infinite Dimensional Complex Analy- sis and Applications is being held at Dongguk University (Gyeongju), continuing to The 16th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (July 28–August 1, 2008; http://16th.icfidcaa.org). This conference is, especially, held as one of satellite conferences of Seoul ICM 2014 whose approval sta- tus no. is 36 and code is ChCh (see http://www.icm2014.org/sc). This conference is, in particular, being held to be joined with a big section [Nonlinear Operator Theory in Functional Analysis] organized mainly by Professor Yeol Je Cho who has held his confer- ences also with a large number of participants almost every two years in Korea more than 7 times, for example, the nearest one, (see http://www.gnu.ac.kr/hb/MINFAA2012/). We are very welcome all participants and contributors from more than 30 countries, for example, Canada, Catar, China, Croatia, Egypt, Finland, France, Germany, Greece, Hungary, India, Iran, Japan, Malaysia, Mexico, Montenegro, Nepal, New Zealand, Os- man, Pakistan, Poland, Romania, Russia, Saudi Arabia, Serbia, Taiwan, Tailand, Turkey, USA, Uzbekistan, Vietnam, and many institutions in Korea. During your stay in Dongguk University, Gyeongju Campus, besides study on your specialties, we are encouraging all of you to enjoy sight-seeing Gyeongju: This Gyeongju, once a capital of a millennium-old Silla Dynasty in Korea, is a historic hometown of Korean spiritual culture, with lots of relics, related especially to Buddhism, as World Cultural Heritages designated by UNESCO. Please use this rare occasion to experience and feel a Korean culture and tradition. Due mainly to a tight and short-period of this conference, we are providing only the afternoon of August 10 for participants to choose to visit a few ones among many historic places. We are giving our sincere gratitude to all participants, especially, those who are pre- senting their valuable research works during this conference, and contributors who are not able to come here, due to unexpected and urgent things to be solved. We thank, whole-heartedly, all members of international and local committee for helping to orga- nize this conference and encourage their students and colleagues to participate in this conference. We should express our deepest thanks to Professor H. M. Srivastava and Ravi P. Agarwal who have introduced, for this conference, two special issues of rather higher impact factor SCIE journals, FILOMAT and Journal of Inequalities and Applications- a SpringerOpen journal (see Thematic series on Recent Advances in Inequalities and Applications from Real and Complex Analysis http://www.journalofinequalitiesandapplications.com/about/update/22ICFIDCAA). We are giving our deep appreciation to all involved staff and Professors in Dongguk University (Gyeongju), and, especially, Professor Dae Ho Jin, for their sincere help to proceed all things regarding this conference smoothly and properly, We also feel deep 2 gratitude to two secretaries (Department of Mathematics Education): Miss Joo Eun Lee and Miss Ye Na Kang for their hard-working and excellent management of all involved miscellaneous things together with about 10 undergraduate volunteers of this Depart- ment. We should express our special and deep thanks for the following institutions for their spiritual and financial support: Dongguk University (Gyeongju Campus); Youngnam Mathematical Society; BK21PLUS Center for Math Research and Education at PNU; Gyeongsang National University; KOFST (The Korean Federation of Science and Tech- nology Societies). Finally the managing organizer (Junesang Choi) would like to express many thanks to each member of his family; Young Sook Ha (his wife), So Young Choi (his lovely daughter), and very specially, Jae-Ho Choi who has helped his father to make the website of this conference and lots of other involved work to prepare for, proceed, and finalize this conference. He must have had many difficulties to prepare for this conference without his son, Jae-Ho’s uniquely devoted help. 3 Committee International Advisory Board Chairman: • Liang Wen Liao (Nanjing University, China)
Vice-chairmen: • Hiroaki Aikawa (Hokkaido University, Japan) • Nak Eun Cho (Pukyong National University, Korea) • Junesang Choi (Dongguk University, Korea) • Akio Kodama (Kanazawa University, Japan) • Tatsuhiro Honda (Hiroshima Institute of Technology, Japan) • Young Joo Lee (Chonnam National University, Korea) • Masaru Nishihara (Fukuoka Institute of Technology, Japan) • Tao Qian (University of Macau, China) • Kwang Ho Shon (Pusan National University, Korea) • Le Hung Son (Hanoi Institute of Technology, Vietnam) • Toshiyuki Sugawa (Tohoku University, Japan) • Chung Chun Yang (Nanjing University, China) Website
Academic Advisory Board • Hari M. Srivastava (University of Victoria, Canada) • Ravi P. Agarwal (Texas A&M University-Kingsville, USA) • Jack R. Quine (Florida State University, USA) • Themistocles M. Rassias (National Technical University of Athens [Zografou Campus], Greece) • Tae Young Seo (Pusan National University, Korea) • Yeol Je Cho (Gyeongsang National University, Korea) 4 Organizing Chairs • Junesang Choi (managing organizer) (Dongguk University, Gyeongju) • Yeol Je Cho (Gyeongsang National University) • Jong Kyu Kim (Gyeongnam University) • Kwang Ho Shon (Pusan National University)
Topics of Conference
• Applied Complex Analysis • Clifford Analysis • Complex Dynamical Systems • Complex Function Spaces and Operator Theory • Complex Numerical Analysis • Functional Analysis Methods in Complex Analysis and Applications to Partial Differential Equations • Qusiconformal Mapping, Riemann Surfaces, Teichmuller Theory and Kleinian Groups • Complex Manifolds • Several Complex Variables • Value Distribution Theory • Special Functions • Number theory • Control and Systems Theory; Process Control; Optimal control • Nonlinear Operator Theory in Functional Analysis • But any other mathematical subject will be gladly welcomed. 5 History of International Conference on Finite or Infinite Dimensional Complex Analysis
History The colloquia originated when many Korean and Japanese mathematicians recognized that they drew only upon the research done in Europe and the United States, without looking at the nearest neighbor countries. With Joji Kajiwara of Kyushu University in Japan as Chairman, they established the Organizing Committee of the Korean-Japanese Colloquium on Finite or Infinite Dimensional Complex Analysis. • Kwang Ho Shon of Pusan National University in Korea held the First Korean- Japanese Colloquium on Finite or Infinite Dimensional Complex Analysis at Pusan National University in July 1993. • Hideaki Kazama of Kyushu University held the Second Colloquium at Kyushu University in July 1994. The committee invited their Chinese colleague Zhong Li of Peking University and extended the name from Korean-Japanese to International. • Suk Young Lee held the Third International Colloquium on Finite or Infinite Dimensional Complex Analysis at Iwha University in Seoul, Korea, July/August 1995. • Tadayoshi Kanemaru held the Fourth Colloquium at Kumamoto University in Japan, August 1996. • Lo Yang of Academia Sinica and Zong Li of Peking University held the Fifth Colloquium at Peking University in Beijing, August 1997. • Ern Gun Kwon of Andong University held the Sixth Colloquium at Andong University in Korea, August 1998. • Masaru Nishihara of Fukuoka Institute of Technology in Japan held the Seventh Colloquium at the Socileducational Center of Fukuoka Prefecture, August 1999. • Lo Yang of Academia Sinica and Hong-Xun Yi of Shandong University held the Eighth Conference on Finite or Infinite Dimensional Complex Analysis at Shandong University (Jinan) - Shandong University of Science and Technology (Taian), August 22 – 26, 2000. • Hung Son Le and Hai Khhoi Le held the Ninth International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, at Hanoi University of Technology, Hanoi, Vietnam, August 8 – 12, 2001. • Kiwon Kim of Silla University held the Tenth International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, at Silla University, Pusan, Korea, July 29 – August 2, 2002. • The Eleventh International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, at Chiang Mai University, Chiang Mai, Thailand, July 27 – 31, 2003. • Mitsuo Morimoto of International Christian University held the Twelfth Inter- national Conference on Finite or Infinite Dimensional Complex Analysis and Applications at International Christian University, Tokyo, Japan, July 27 – 31, 2004. 6
• Hasi Wulan of Shantou University held the Thirteenth International Conference on Finite or Infinite Dimensional Complex Analysis and Applications at Shantou Christian University, Shantou, China, August 8 – 12, 2005. • Le Hung Son of Hanoi University of Technology held the Fourteenth International Conference on Finite or Infinite Dimensional Complex Analysis and Applications at Hue, Vietnam, August 1– 5, 2006. • Yoichi Imayoshi of Osaka City University held the Fifteenth International Con- ference on Finite or Infinite Dimensional Complex Analysis and Applications at Osaka City University, Tokyo, Japan, July 30 – August 3, 2007. • Junesang Choi held the sixteenth International Conference on Finite or Infi- nite Dimensional Complex Analysis and Applications at Dongguk University, Gyeongju, Korea, July 28 – August 1, 2008. • Le Hung Son of Hanoi University of Technology held the Seventeenth Inter- national Conference on Finite or Infinite Dimensional Complex Analysis and Applications at Ho Chi Minh City, Vietnam, On August 3–7, 2009. • Tao Qian of University of Macau held The eighteenth International Conference on Finite or Infinite Dimensional Complex Analysis and Applications at University of Macau, Macau, China, on August 13–17, 2010. • Toshiyuki Sugawa of Tohoku University held The nineteenth International Con- ference on Finite or Infinite Dimensional Complex Analysis and Applications in Hiroshima, Japan, on December 11–15, 2011. • Le Hung Son of Hanoi University of Science and Technology held the twentieth International Conference on Finite or Infinite Dimensional Complex Analysis and Applications in Hanoi, Vietnam, On July 29–August 3, 2012. • Liangwen Liao of Nanjing University held the 21st International Conference on Finite or Infinite Dimensional Complex Analysis and Applications in Nanjing, China, On June 15–19, 2013. • Junesang Choi of Dongguk University is holding The 22nd International Con- ference on Finite or Infinite Dimensional Complex Analysis and Applications at Dongguk University, Gyeongju, Korea, on August 8–11, 2014. This conference is, in particular, being held to be joined with a big section [Nonlinear Opera- tor Theory in Functional Analysis] organized mainly by Professor Yeol Je Cho who has held his conferences also with a large number of participants almost every two years in Korea more than 7 times, for example, the nearest one, (see http://www.gnu.ac.kr/hb/MINFAA2012/)
Publications • Finite or Infinite Dimensional Complex Analysis (Proceedings of the Seventh International Colloquium), edited by Joji Kajiwara, Zhong Li, Kwang Ho Shon, Lecture Notes in Pure and Applied Mathematics, Volume 214, Marcel Dekker, Inc., 2000. • Proceedings of the Eighth International Colloquium on Finite or Infinite Di- mensional Complex Analysis, edited by Lo Yang and Hong-Xun Yi, Shangdong Science and Technology Press, 2001. 7
• Proceedings of the Tenth International Conference on Finite or Infinite Dimen- sional Complex Analysis and Application, Busan, Korea, July 29 – August 2, 2002. Edited by J. Kajiwara, K.W. Kim and K.H. Shon, Silla University, April 2003. • Proceedings of the 12th International Conference on Finite and Infinite Dimen- sional Complex Analysis and Applications, edited by Hideki kazama, Mitsuo Morimoto, Chung-Chun Yang, Kyushu University Press, 2005. • Proceedings of the 13th International Conference on Finite and Infinite Dimen- sional Complex Analysis and Applications, edited by Yuefei Wang, Shengjian Wu, Hasi Wulan, and Lo Yang, the World Scientific Publishing Co., 2006. • Complex Analysis and its Applications, edited by Yoichi Imayoshi, Yohei Komori, Masaharu Nishio, Ken-ichi Sakan, Osaka Municipal Universities Press, Ocami Studies Volume 2, 2007. • Proceedings of the 16th International Conference on Finite and Infinite Dimen- sional Complex Analysis and Applications, edited by Junesang Choi, SoYoung Choi, Dae Ho Jin, Seong-A Kim, and Jong Moon Shin, Daeyang Printing, Gyeongju, Korea, 2009. • Algebraic Structures in Partial Differential Equations Related to Complex and Clifford Analysis, Proceedings of the 17th International Conference on Finite and Infinite Dimensional Complex Analysis and Applications, held in HoChiMinh City, 2009, edited by Le Hung Son and Wolfgang Tutschke, HoChiMinh City University of Education Press, 2010. • Topics in Finite or Infinite Dimensional Complex Analysis and its Applications, Proceedings of the 19th International Conference on Finite and Infinite Dimen- sional Complex Analysis and Applications, held in Hiroshima, 2011, edited by K. Matsuzaki and T. Sugawa, Tohoku University Press, 2012. • Interactions between Real and Complex Analysis, Proceedings of the 20th Inter- national Conference on Finite and Infinite Dimensional Complex Analysis and Applications, held in Hanoi, 2012, edited by Le Hung Son and Wolfgang Tutschke, Science and Technics Publishing House, 2012. • For The 22nd ICFIDCAA, two special issues of rather higher impact factor SCIE journals, FILOMAT and Journal of Inequalities and Applications-a SpringerOpen journal (see Thematic series on Recent Advances in Inequalities and Applications from Real and Complex Analysis http://www.journalofinequalitiesandapplications.com/about/update/22ICFIDCAA), have been introduced. 8 Welcome Address
Lee, Gye-Young President of Dongguk University Gyeongju Campus August 9, 2014
Very welcome: Excellent researchers in mathematics and their family members from more than 30 countries. Since the first conference in 1993, today, I feel a great honor and give a sincere con- gratulations to hold the 22nd International Conference on Finite or Infinite Dimensional Complex Analysis and Applications in this Dongguk University, Gyeongju Campus. I strongly believe that your talks and discussions to be presented here by famous mathematicians from Canada, Catar, China, Croatia, Egypt, Finland, France, Ger- many, Greece, Hungary, India, Iran, Japan, Malaysia, Mexico, Montenegro, Nepal, New Zealand, Osman, Pakistan, Poland, Romania, Russia, Saudi Arabia, Serbia, Taiwan, Tailand, Turkey, USA, Uzbekistan, Vietnam, and many institutions in Korea, for 4 days, will be able to give a great contribution in making a considerable progression on mathematics as well as its related modern science and technology. I would like to give a brief history of Dongguk University. In 1906, Dongguk University in Seoul was founded under the spirit of Buddhism by a group of pioneering buddhists. Now it has grown to become a rather big University with 4 campuses, which are located in Seoul, Gyeongju, Ilsan and Los Angeles. In 1978, this Gyeongju Campus was founded for the purpose of combining spiritual culture and scientific civilization in a harmonious way, in this Gyeongju, a capital of a millennium-old Silla Dynasty in the Korean history. As of this year 2014, we are celebrating the 36th Anniversary. Gyeongju Campus has 9 colleges including College of Oriental Medicine and College of Medicine. This campus has 9,500 students counting graduate students. Even though Dongguk University was founded by the spirit of Buddhism, each campus has always been open to students with a variety of faiths and philosophies. During your stay in Dongguk University, Gyeongju Campus, besides study on your specialties, I am encouraging all of you to enjoy sight-seeing Gyeongju: This Gyeongju, a capital of a millennium-old Silla Dynasty in Korea, is a historic hometown of Korean spiritual culture, with lots of relics, related especially to Buddhism, as World Cultural Heritages designated by UNESCO. Please use this rare occasion to experience and feel a Korean culture and tradition. Finally I would like to give my sincere thanks to all staffs of College of Education for giving their devotion to prepare for this conference and also my deepest thanks to the Korean Federation of Science and Technology Societies, Youngnam Mathematical Soci- ety, BK21PLUS Center for Math Research and Education at Pusan National University, Gyeongsang National University, and all other personal supporters for their financial aids. 9
I hope all of you will be able to return to your places with a good memory ever lasting through your lives and a good health. Again, welcome all participants and I am offering my heartful congratulations to the success of 22nd ICFIDCAA. Thanks.
Outline of Activities
August 7
• Registration will be begun at the first floor of the dormitory building from 10:00, for participants who are planned to arrive here on August 7 or before
• Registration will be continued at the place of the main administration building (our conference place), for participants who are planned to arrive here on August 8 or after.
August 8
Morning Section (9:30–12:00)
• Registration
• Opening Ceremony
• Two Plenary Talks
Lunch and Rest (12:00–13:20)
Afternoon Section
Invited Talks (13:30–17:05) 10
• Dinner (18:00–)
August 9
Morning Section (9:30–12:00)
• Registration
• Welcome Address, President of Dongguk University
• Three Plenary Talks
Lunch and Rest (12:00–13:20)
Afternoon Section Invited Talks (13:30–17:05)
• Banquet (18:00–20:30)
August 10
Morning Section (9:00–11:35) Invited Talks
Lunch and Rest (11:40–12:40)
Afternoon Section
• Sightseeing in Gyeongju (13:00–17:40) 11
• Dinner (18:00–)
August 11
Morning Section (9:00–11:40) Invited Talks
Lunch and Rest (12:00–13:20)
Afternoon Section Invited Talks (13:30–17:05)
Dinner (18:00–)
August 12
A tour bus will wait next to The Statue of Elephant and will start this Dongguk University at 10:00 in the morning for Seoul ICM2014 and its related dormitory. So each participant who make a reservation for the tour bus should get on this bus until 9:40. 12 Details of Activities
August 7
• Registration will be begun at the first floor of the dormitory building from 10:00, for participants who are planned to arrive here on August 7 or before
• Registration will be continued at the place of the main administration building (our conference place), for participants who are planned to arrive here on August 8 or after.
August 8
Morning Section (9:30–12:00)
• Registration
• Opening Ceremony
• Two Plenary Talks
1. [10:30–11:10] Yeol Je Cho, Approximating fixed points of nonlinear mappings
2. [11:15–11:55] H. M. Srivastava, Some general families of Hurwitz-Lerch Zeta functions and their applications
Lunch and Rest (12:00–13:20)
Afternoon Section
Invited Talks
Section 1 13
1. [13:30-13:50] Liangwen Liao, The complex differential and difference equa- tions and their applications
2. [13:55-14:15] Toshiyuki Sugawa, Extremal problems for close-to-convex func- tions
3. [14:20-14:40] Makoto Masumoto, Holomorphic mappings of once-holed tori into Riemann surfaces of positive genus
4. [14:45-15:05] Seong-A Kim∗, Jinxi Ma and William Ma, Estimates of the hyperbolic metric on the twice punctured plane
5. [15:30-15:50] A. Okay C¸elebi∗ and Umit¨ Aksoy, Dirichlet problem for higher-order nonlinear complex partial differential equations in an unbounded do- main
6. [15:55-16:15] Tatsuhiro Honda, Growth and distortion theorems on a ho- mogeneous unit ball
7. [16:20-16:40] Ikkei Hotta, Chordal Loewner chains with quasiconformal ex- tensions
8. [16:45-17:05] Jongho Yang∗, Boo Rim Choe, Hyungwoon Koo and Maofa Wang, Compact linear combinations of composition operators induced by linear fractional maps
Section 2
1. [13:30-13:50] J. R. Quine, Use of quaternions in molecular biology 14
2. [13:55-14:15] Kwang Ho Shon, The regularity of functions on dual split quaternions
3. [14:20-14:40] Umit¨ Aksoy, Dirichlet Problem for higher order Poisson equa- tion in Clifford analysis
4. [14:45-15:05] Choonkil Park, Quadratic ρ-functional inequalities and equa- tions
5. [15:30-15:50] Dong Yun Shin, Choonkil Park, Reza Saadati and Themis- tocles M. Rassias, A fixed point approach to the fuzzy stability of an AQCQ- functional equation
6. [15:55-16:15] Afrah AN Abdou and Mohamed A Khamsi, On the fixed points of nonexpansive maps in modular metric spaces
7. [16:20-16:40] Dmitry V. Dolgy, Control of the systems subjected by interval perturbation
8. [16:45-17:05] Yan Yang, Stronger uncertainty principles for quaternion Fourier transforms
Section 3
1. [13:30-13:50] Yoshihiro Mizuta, Sobolev’s inequality in Herz-Morrey spaces of variable exponent and duality
2. [13:55-14:15] Dmitrii Karp, Distributional G-function and representations of generalized hypergeometric functions 15
3. [14:20-14:40] Poom Kumam, On best proximity point theorems in metric spaces
4. [14:45-15:05] Eun-Young Lee, Unitary orbits and decompositions of positive matrices
5. [15:30-15:50] Gyungsoo Woo, Robert V. Namm∗ and Svetlana V. Anosova, Sensitivity functions in conditional convex optimization problem
6. [15:55-16:15] Shinuk Kim, Ovarian cancer subtype classification using mi- croRNA and their target mRNA
7. [16:20-16:40] Sebahattin Ikikardes and Recep Sahin, On the extended Hecke groups
8. [16:45-17:05] Kanhaiya Jha, On some compatible type mappings in metric space
• Dinner (18:00–)
August 9
Morning Section (9:30–12:00)
• Registration
• Welcome Address, President of Dongguk University
• Three Plenary Talks
1. [9:45–10:25] Hidetaka Hamada, Extreme points and support points as- n sociated with univalent subordination chains in C 16
2. [10:30–11:10] Vesna Manojlovi´c, Bilipschicity of quasiconformal har- monic mappings
3. [11:15–11:55] Hiroaki Aikawa, Extended Harnack inequalities with ex- ceptional sets and its applications
Lunch and Rest (12:00–13:20)
Afternoon Section Invited Talks
Section 1
1. [13:30-13:50] Pei Dang, Sharper uncertainty principle in signal analysis
2. [13:55-14:15] Ki Won Kim, On weak Bloch functions
3. [14:20-14:40] Kit Ian Kou and Joao Morais, Asymptotic behavior of the quaternion linear canonical transform and the Bochner-Minlos theorem
4. [14:45-15:05] Young Joo Lee, A Coburn type theorem for Toeplitz operators on the Dirichlet space
5. [15:30-15:50] Le Hung Son, Multi-monogenic functions taking value in Clif- ford algebra depending on parameters
6. [15:55-16:15] Masahiro Yanagishita, Weil-Petersson metric on square in- tegrable Teichm¨uller spaces
7. [16:20-16:40] Yu Seon Jang, Taekyun Kim, Hyuck-In Kwon and Jong- Jin Seo, q-Changhee and Boole polynomials 17
8. [16:45-17:05] Katsuhiko Matsuzaki, A certain circle diffeomorphism with H¨oldercontinuous derivative
Section 2
1. [13:30-13:50] Jitsupa Deepho and Poom Kumam, The shrinking projec- tion method for solving the split feasibility, fixed point and system of equilibrium problems
2. [13:55-14:15] M. B. Ghaemi and H. Majani, Stability of functional equa- tions in non-Archimedean spaces
3. [14:20-14:40] Hark-Mahn Kim and Juri Lee∗, Hyers–Ulam stability of homomorphisms and derivations on normed Lie triple systems
4. [14:45-15:05] Hark-Mahn Kim and Eunyoung Son∗, Generalized Hyers– Ulam stability of functional inequalities
5. [15:30-15:50] Yun-Ho Kim and Ji Soo Lee∗, Existence and multiplicity of solutions for equations involving nonhomogeneous operators of p-Laplace type in N R
6. [15:55-16:15] Yun-Ho Kim and Kisoeb Park∗, Existence of solutions for a Neumann problem involving nonhomogeneous operators of the p(x)-Laplace type
7. [16:20-16:40] Yun-Ho Kim and Seung Dae Lee∗, Multiple solutions for N the p(x)-Laplace type operator in R
8. [16:45-17:05] In-Sook Kim and Jung-Hyun Bae∗, Eigenvalues of maximal monotone operators 18 Section 3
1. [13:30-13:50] Tibor K. Pog´any, Alternating Mathieu series and their gen- eralized Omega functions
2. [13:55-14:15] Rekha Srivastava, Some families of extended Pochhammer symbols and their applications involving hypergeometric generating functions
3. [14:20-14:40] Praveen Agarwal, Certain recent fractional integral inequal- ities associated with pathway fractional integral operator
4. [14:45-15:05] Jin-Woo Son, Identities of symmetry for the higher order q- Bernoulli polynomials
5. [15:30-15:50] Jung Rye Lee, Choonkil Park, Cihangir Alaca and Dong Yun Shin, A fixed point approach to the stability of an AQCQ-functional equa- tion in RN-spaces
6. [15:55-16:15] Yong Sup Kim and Arjun Kumar Rathie, Further applica- tions of the generalized Kummer summation theorem for the series 2F1
7. [16:20-16:40] Naoya Hayashi and Yutaka Matsui∗, Decomposition formu- lae for generalized hypergeometric functions with the Gauss-Kummer identity
8. [16:45-17:05] Mustafa Alkan and Yilmaz Simsek, Decomposition of inter- polation functions for the generalized Bernoulli type numbers
• Banquet (18:00–20:30) 19 August 10
Morning Section (9:00–11:35) Invited Talks
Section 1
1. [9:00-9:20] Abhijit Banerjee, Some investigations on the uniqueness of mero- morphic function sharing one value with its derivative
2. [9:25-9:45] Sanjib Kumar Datta, On the (p, q)-th relative order oriented growth properties of entire functions
3. [9:50-10:10] Moonja Jeong, Some results regarding the Schwarz lemma about the boundary fixed points
4. [10:25-10:45] Stanislawa Kanas, Pythagorean means and differential subor- dinations
5. [10:50-11:10] Yuri Dymchenko, The condition of small girth for the moduli of curves on Finsler spaces
6. [11:15-11:35] Jaewon Lee, Half lightlike submanifolds of a semi-Riemannian manifold of quasi-constant curvature
Section 2 20
1. [9:00-9:20] Makoto Abe, A cohomological characterization for Stein open sets in a 2-dimensional Stein orbifold
2. [9:25-9:45] Djurdje Cvijovi´c, Integral–valued polynomials associated with finite trigonometric sums
3. [9:50-10:10] J. Y. Kang∗ and C. S. Ryoo, A research of symmetry on the twisted Genocchi polynomials with weak weight α
4. [10:25-10:45] Abdelmejid Bayad, Zetas functions and multiplicative parti- tion theory
5. [10:50-11:10] Abdelmejid Bayad, Nazli Yildiz Ikikardes and Daeyeoul Kim, A study of convolution sums of divisor functions
6. [11:15-11:35] Ismail Naci Cangul, Muge Togan, and Aysun Yurttas, Zagreb indices and coindices of double graphs of certain graph types
Section 3
1. [9:00-9:20] Mohammad S. R. Chowdhury∗ and Yeol Je Cho, Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators in non-compact settings
2. [9:25-9:45] B. A. Case∗ and Y. M. Guan, Actuarial science education in mathematics departments
3. [9:50-10:10] Yun-Ho Kim and Eun Bee Choi∗, Existence of at least three solution for equations involving nonhomogeneous operators of p-Laplace type in N R 21
4. [10:25-10:45] In-Sook Kim, Some surjectivity results on maximal monotone operators
5. [10:50-11:10] Parin Chaipunya, Yeol Je Cho, and Poom Kumam, On common selectors for a continuum of set-valued maps and its fixed points
6. [11:15-11:35] Yun-Ho Kim and Byung-Hoon Hwang∗, Global Bifurcation result for a class of equations involving p(x)-Laplace type
Lunch and Rest (11:40–12:40)
Afternoon Section
• Sightseeing in Gyeongju (13:00–17:40)
• Dinner (18:00–)
August 11
Morning Section (9:00–11:40) Invited Talks
Section 1
n 1. [9:00-9:20] E. G. Kwon, Mean Lipschitz spaces on the unit ball of C
2. [9:25-9:45] Adel A. Attiya, Some applications of Mittag-Leffler function in the unit disk 22
3. [9:50-10:10] Ji Hyang Park∗ and Nak Eun Cho, Notes on multivalently meromorphic starlikeness
4. [10:25-10:45] Ohsang Kwon, On the argument properties of analytic func- tions with fixed second coefficients
5. [10:50-11:10] Young Jae Sim and Oh Sang Kwon, A certain subclass of meromorphic functions
6. [11:15-11:35] Fengrong Zhang∗, Nana Liu, and Weiran L¨u, Entire solu- tions of certain class of differential-difference equations
Section 2
1. [9:00-9:20] Jong Kyu Kim, Viscosity approximation method with Meir- Keeler contractions viscosity approximation method with Meir-Keeler contrac- tions
2. [9:25-9:45] Jong Soo Jung, A hybrid iterative algorithm for inverse-strongly monotone mappings and strictly pseudocontractive mappings
3. [9:50-10:10] Young-Ho Kim, A note on the almost sure and moment exponential stability for stochastic functional differential equations
4. [10:25-10:45] Min Zhang, C∞-Solutions for the p-order Feigenbaum’s func- tional equation h(g(x)) = gp(h(x))
5. [10:50-11:10] Yuanyuan Wang, Bifurcation of numerical discretization in a complex amplitude equation with delayed feedback 23
6. [11:15-11:35] Tatiana Kalmykova and Vladimir Shlyk∗, On the problem of decomposition and composition of normal ring open sets
Section 3
1. [9:00-9:20] Mohammad S. R. Chowdhury∗ and Yeol J Cho, Generalized quasi-variational inequalities for pseudo-monotone type III and strongly pseudo- monotone type III operators on non-compact sets
2. [9:25-9:45] Phayap Katchang, Modified mann iterative for variational in- equality problem and common fixed point problems of nonexpansive mappings and nonexpansive semigroups in q-uniformly smooth Banach spaces
3. [9:50-10:10] Aphinat Ninsri and Wutiphol Sintunavarat, Common fixed point results for gα-approximative multivalued mappings in metric spaces
4. [10:25-10:45] Supak Phiangsungnoen and Poom Kumam, Fuzzy stability of radical quartic functional equation via fixed point approach
5. [10:50-11:10] Plern Saipara and Poom Kumam, On fixed point algorithm for solving the constrained convex optimization problem
6. [11:15-11:35] Wutiphol Sintunavarat, A new approach to (α, ψ)-contractive mappings and generalized Ulam-Hyers stability, well-posedness and limit shadow- ing
Section 4 24
1. [9:00-9:20] A. Kılı¸cman, Generating fractional partial differential equations with variable coefficients via convolutions
2. [9:25-9:45] Akos´ Pint´er, Resolution of nontrivial diophantine equations with- out reduction methods
3. [9:50-10:10] Arjun K. Rathie, Generalizations of Preece’s and Bailey’s hypergeometric identities involving products of generalized hypergeometric series with applications
4. [10:25-10:45] M. Kh. Ruziev, On a problem with two non-local boundary conditions for the degenerated elliptic type equation with singular coefficient and spectral parameter
5. [10:50-11:10] Xiaoxia Wang, Five patterns of terminating summation for- mulas 3F2
6. [11:15-11:35] Bing Xiao, Qifeng Wu and Weiling Xiong, Some normal criteria for families of meromorphic functions
Section 5
1. [9:00-9:20] Hemant Kumar Nashine, Common fixed point theorems under generalized W-weakly contractive condition
2. [9:25-9:45] Mehmet Ali O¨ zarslan and Tuba Vedi, Two dimensional Chlodowsky variant of q-Bernstein-Schurer-Stancu operators
3. [9:50-10:10] Nilufar Rakhmatullaeva, Non-local boundary value problem for mixed parabolic-hyperbolic type equation 25
4. [10:25-10:45] Luis Manuel Tovar, Hyperbolic Fg(p; q; s) and Fφ(p; q; s) classes
5. [10:50-11:10] Shuhuang Xiang, Implicit solution function and least-norm time-stepping scheme for Z-matrix linear complementarity systems
6. [11:15-11:35] Yonghong Yao, The split common fixed point problem for the pseudo-contractive and quasi-nonexpansive mappings
Lunch and Rest (12:00–13:20)
Afternoon Section
Section 1
1. [13:30-13:50] Masaru Nishihara, Holomorphic extensions of invariant holomorphic functions with a complex Lie group action
2. [13:55-14:15] Veli Kurt and Burak Kurt, Some identities and recurrence relations on the two variables Bernoulli, Euler and Genocchi polynomials
3. [14:20-14:40] E. T. Karimov, On some applications of special functions to the investigation of boundary-value problems for PDEs
4. [14:45-15:05] Shilpi Jain, Integrals containing Laguerre type polynomials and Bessel functions
5. [15:30-15:50] Qiu-Ming Luo, The history and study for Ramanujan’s circu- lar summation 26
6. [15:55-16:15] Feng Qi and Wen-Hui Li, Integral representations and prop- erties of some functions involving the logarithmic function
7. [16:20-16:40] Yilmaz Simsek, Remarks on combinatorial identities related to special polynomials
8. [16:45-17:05] Zhi-Bo Huang, On q-difference Riccati equation and q-Gamma function
Section 2
1. [13:30-13:50] Hacer Ozden and Yilmaz Simsek, On multiplication for- mula of the modification and unification of Apostol-type polynomials
2. [13:55-14:15] Su Hu, The (S, {2})-Iwasawa theory
3. [14:20-14:40] Min-Soo Kim, On p-adic analogue of Weil’s elliptic functions according to Eisenstein
4. [14:45-15:05] Elena Prilepkina, Quadratic forms involving Neumann func- tion
5. [15:30-15:50] Gradimir V. Milovanovi´c, Generalized quadrature formulae and multiple orthogonal polynomials
6. [15:55-16:15] Gue Myung Lee∗ and Tien Son Pham, On stability results for perturbed polynomial optimization problems 27
7. [16:20-16:40] A. G. Aleksandrov, Differential forms and homological cal- culus
8. [16:45-17:05] Guowu Yao, On geodesic geometry in (asymptotic) Teichm¨uller spaces
Section 3
1. [13:30-13:50] Wenjun Yuan, Zifeng Huang, Maozhun Fu and Jianming Qi, Several recent results regarding the meromorphic solutions of some algebraic differential equations and its applications
2. [13:55-14:15] Wenjun Yuan, Bing Xiao and Yonghong Wu, The general traveling wave solutions of the Fisher type equations and some related problems
3. [14:20-14:40] Uamporn Witthayarat∗, Kriengsak Wattanawitoon and Poom Kumam, Iterative algorithm for solving fixed point problem and bilevel generalized mixed equilibrium problem in Banach space
4. [14:45-15:05] Kriengsak Wattanawitoon∗ and Uamporn Witthayarat, A new approximating scheme for solving fixed point problem and bilevel mixed equilibrium problem in Hilbert spaces
5. [15:30-15:50] Oratai Yamaod and Wutiphol Sintunavarat, Fixed point theorems for new generalized nonlinear contraction mappings in multiplicative metric spaces
6. [15:55-16:15] Kittipong Wongkum, Parin Chaipunya, and Poom Ku- mam, On the stability of the functional equation in modular spaces 28
7. [16:20-16:40] Chirasak Mongkolkeha∗, Tamaki Tanaka and Poom Ku- mam, Ekeland’s variational principle and fixed point theorems in quasi-partial metric spaces
8. [16:45-17:05] Junesang Choi, Rakesh K. Parmar∗ and Purnima Chopra, H H The incomplete Srivastava’s triple hypergeometric functions γB and ΓB
Section 4
1. [13:30-13:50] Dae Ho Jin, Special lightlike hypersurfaces of indefinite Kaehler manifolds
2. [13:55-14:15] Andrea Huszti, Bilinear pairings and their applications
3. [14:20-14:40] S´ebastienGaboury, Several expansion formulas involving the ∗ generalized Hurwitz-Lerch zeta function Φµ(z, s, a) with applications to Apostol- type polynomials
4. [14:45-15:05] I. A. Shilin and Junesang Choi, Bases transforms in SO(3, 1)- and SO(2, 2)-representation spaces and formulas for related special functions
5. [15:30-15:50] Junesang Choi, Several recent results regarding the Riemann zeta function ζ(s)
Section 5 29
1. [13:30-13:50] Ravi P. Agarwal, Boundary value problems for delay differ- ential equations
2. [13:55-14:15] Jiawei Chen, Bilevel vector pseudomonotone equilibrium prob- lems
3. [14:20-14:40] Sun Young Cho, Shin Min Kang and and Xiaolong Qin, On zeros of the sum of two monotone operators in Hilbert spaces
4. [14:45-15:05] Q-Heung Choi, Reduction method for a class of the semilinear elliptic systems
5. [15:30-15:50] Mohammad Farid, Existence and iterative approximation of solutions of generalized mixed vector equilibrium problems in a Banach space
6. [15:55-16:15] Tacksun Jung, Four solutions for the Hamiltonian system 30 Abstracts of Talks
On the fixed points of nonexpansive maps in modular metric spaces
Afrah AN Abdou1 and Mohamed A Khamsi2,3 1 Department of Mathematics, King Abdulaziz University P.O. Box 80203, Jeddah, 21589, Saudi Arabia E-Mail: [email protected] 2Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas, USA 3Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals Dhahran, 31261, Saudi Arabia E-Mail: [email protected]
The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, have been recently introduced. In this paper we investigate the existence of ?xed points of modular nonexpansive mappings. We also discuss some compactness properties of the family of admissible sets in modular metric spaces with uniform normal structure property. 2010 MSC. Primary 47H09; Secondary 46B20, 47H10, 47E10
A cohomological characterization for Stein open sets in a 2-dimensional Stein orbifold
Makoto Abe Division of Mathematical and Information Sciences Faculty of Integrated Arts and Sciences Hiroshima University Higashi-Hiroshima, 739-8521, Japan E-Mail: [email protected] 31
We say that a complex space X is an orbifold if every point p ∈ Sing (X) is a quotient singular point. Let D be an open set of a Stein orbifold of pure dimension 2. Then, the following three conditions are equivalent. (1) D is Stein. (2) D is meromorphically convex. (3) The canonical homomorphism H1(D, O) → H1(D, M) is a zero map.
2010 MSC. 32E10, 32C55, 32L10.
Certain recent fractional integral inequalities associated with pathway fractional integral operator
Praveen Agarwal Department of Mathematics Anand International College of Engineering Jaipur-303012, India E-Mail: [email protected]; [email protected]
In the last few decades, fractional integral inequalities have proved to be one of the most powerful and far-reaching tools for the development of many branches of pure and applied mathematics. Very recently, number of authors have presented some generalized inequalities involving the fractional integral operators. Here, using Pathway fractional integral operator, we give some(presumably) new fractional integral inequalities whose special cases are shown to yield corresponding inequalities associated with Riemann- Liouville type fractional integral operators. Relevant connections of the results presented here with those earlier ones are also pointed out. 2010 MSC. 26D10; 26A33. 32
Boundary value problems for delay differential equations
Ravi P. Agarwal Department of Mathematics, Texas A&M University - Kingsville, 700 University Blvd., Kingsville, TX 78363-8202, USA E-Mail: [email protected]
We develop an upper and lower solution method for second order boundary value problems for nonlinear delay differential equations on an infinite interval. Sufficient conditions are imposed on the nonlinear term which guarantee the existence of a solution between a pair of lower and upper solutions, and triple solutions between two pairs of upper and lower solutions. An extra feature of our existence theory is that the obtained solutions may be unbounded.Two examples which show how easily our existence theory can be applied in practice are also illustrated.
Extended Harnack inequalities with exceptional sets and its applications
Hiroaki Aikawa Department of Mathematics, Hokkaido University Sapporo 060-0810, Japan E-Mail: [email protected]
The Harnack inequality is one of the most fundamental inequalities for positive har- monic functions and, it is extended for positive solutions to general elliptic equations and parabolic equations. In this talk we give a different view point of generalization. We generalize Harnack chains rather than equations. More precisely, we allow a small ex- ceptional set; and yet we obtain a similar Harnack inequality. The size of an exceptional set is measured by capacity. The results are new even for classical harmonic functions. Our extended Harnack inequality includes information for the boundary behavior of positive harmonic functions. It yields a boundary Harnack principle for a domain whose boundary is given locally by the graph of a function with modulus of continuity worse than H¨oldercontinuity. Also, it has an application to the Dirichlet heat kernel estimate. We say that the Dirichlet heat kernel is intrinsic ultracontractive (IU) if the heat kernel 33 is bounded above and below by the product of the ground states modulo positive multi- plicative constants depending on time. With the aid of the extended Harnack inequality, we show IU for a very nasty domain given by the graph of a u.s.c. function with some integral condition. We are very much stimulated by probabilistic ideas, although our arguments are purely analytic and elementary. 2010 MSC. Primary 31B05, 35K08; Secondary 60J45.
Dirichlet Problem for higher order Poisson equation in Clifford analysis
Umit¨ Aksoy Department of Mathematics, Atilim University Ankara, Turkey E-Mail: [email protected]
Using integral representation formulas in terms of the powers of Laplacian in the com- plex Clifford algebra Cm for m ≥ 3, we give the solution of the Dirichlet problem for higher order Poisson equation in the unit ball.
2010 MSC. Primary 31B30; Secondary 31B10, 30G35.
Differential forms and homological calculus
A. G. Aleksandrov Institute of Control Sciences, Russian Academy of Sciences Profsoyuznaya str. 65, B-342, GSP-7, Moscow, 117997 Russian Federation E-Mail: ag [email protected] 34
In the preamble to his famous article “On the De Rham cohomology of algebraic vari- eties” (Publ. l’I.H.E.S.´ 29 (1966), 95–103) A.Grothendieck writes: “... we can consider • the complex of sheaves ΩX/k of regular differentials on X, the differential operator being of course the exterior differentiation ...” He called this (increasing) complex De Rham complex although it was first considered and studied already by H.Poincar´e(thus, in the case of manifolds we should mention the classical Poincar´elemma). However, along with the structure of a complex, given by the exterior differentiation, one can endow the family of sheaves of regular differential forms with a structure of a • complex in other ways. For example, similarly to the De Rham complex (ΩX/k, d), we • can consider another increasing complex (ΩX/k, δ), where the differential δ is the operator 1 of exterior multiplication by a K¨ahler form ω ∈ ΩX , i.e. δ = ∧ω. On the other hand, if there exists a regular vector field V on X, then the contraction of differential forms along the vector field V equips the family with the structure of a decreasing complex • (ΩX/k, ιV ). Analogously, making use of the Poisson bracket and the contraction along a • bi-vector field W, we can define a decreasing complex (ΩX/k, ∂W ) on Poisson varieties, etc. If X is a manifold, then the sheaves of regular forms are locally free. In that case, for • instance, the complex (ΩX/k, ιV ) is locally isomorphic to the classical Koszul complex • and the complex (ΩX/k, δ) is its dual; it is well-known that these complexes are locally isomorphic. If X has singularities, then, in general, the theory is considerably more difficult than in the classical case, both complexes belong to the class of the generalized Koszul complexes. In the talk, we describe an approach to computing the Euler characteristic, the homol- ogy and cohomology groups of the above-mentioned complexes which contain important information about the variety and its singularities, topological and analytical structure of the variety, its basic invariants, etc. We also discuss some applications in complex analysis and geometry, topology and dynamical systems, classical mechanics and other fields of natural sciences. 2010 MSC. Primary 14F10; Secondary 13D07, 14F40, 32S65.
Decomposition of interpolation functions for the Generalized Bernoulli type numbers
Mustafa Alkan and Yilmaz Simsek Akdeniz University Faculty of Science Department of Mathematics Antalya 07058, Turkey 35
E-Mail: [email protected] and [email protected]
The goal of this paper is to construct decomposition of Dirichlet type L-function with any characters on the finite groups. These functions interpolate generalized Bernoulli type numbers associated with any character. We give some properties of these functions, character and numbers. 2010 MSC. 11S40, 11S80, 11B68.
Some applications of Mittag-Leffler function in the unit disk
Adel A. Attiya Department of Mathematics, Faculty of Science University of Mansoura, Mansoura 35516, Egypt E-Mail: [email protected]
The importance of Mitttag-Leffler function due to its involvement in many problems in natural and applied science. In this paper we introduce an operator associated with generalized Mittag-Leffler function in the unit disk U = {z : |z| < 1}. By using this operator and the virtue of differential subordination, we obtain interesting results. Some applications of our results are also discussed. 2010 MSC. 30C45; 30C80; 33E12.
Some investigations on the uniqueness of meromorphic function sharing one value with its derivative
Abhijit Banerjee Department of Mathematics, University of Kalyani, Nadia 36
West Bengal 741235, India. E-Mail: abanerjee [email protected]
Value distribution theory of meromorphic functions, is one of the most important achievements in the preceding century to understand the properties of meromorphic functions. In this theory one studies how an entire or a meromorphic function assumes some values and the influence of assuming certain values in some specific manner on a function. Now-a-days the uniqueness theory of meromorphic functions, essentially developed along with the Nevanlinna theory, is an extensive as well as active subfield of value distribution theory. This theory mainly studies conditions under which there exists essentially only one function satisfying the prescribed conditions. It is well known that a non-constant polynomial is determined by its zeros but this will not conform in the case of transcendental entire or meromorphic functions. So how to determine uniquely a meromorphic function is interesting although sophisticated. In 1996, Considering the uniqueness problem of an entire function sharing one value with its derivative, the following famous conjecture was proposed by Br¨uck [1] Conjecture: Let f be a non-constant entire function such that the hyper order ρ2(f) of f is not a positive integer or infinite. If f and f 0 share a finite value a CM, then 0 f −a f−a = c, where c is a non zero constant. Br¨uck himself proved the conjecture for a = 0. Since then a large number of authors judiciously investigated the special forms of the conjecture with additional suppositions. From the conclusion of Br¨uck’s result and its subsequent ones, we see that for an ap- propriate constant or small function a, the relation between a function f and its k-th f (k)−a derivative counterpart are determined by f−a = c for some constant c ∈ C/{0}. In particular, if c = 1 then f = f (k), which gives more specific form of the function. K.T.Yu [2] was the first to show that the above specific type of relation between an entire or non entire meromorphic function with its k-th derivative counterpart holds without assuming any restriction on the growth of the function. In this talk, we propose to highlight the gradual development on the results of Br¨uck and Yu and the scope for future investigations.
References [1] R. Br¨uck, On entire functions which share one value CM with their first derivative, Results in Math., 30(1996), 21-24. [2] K. W. Yu, On entire and meromorphic functions that share small functions with their derivatives J.Inequal.Pure Appl. Math., 4(1)(2003), Art.21 [ONLINE http://jipam.vu.edu.au/].
2010 MSC. Primary 30D35. 37
Zetas functions and multiplicative partition theory
Abdelmejid Bayad Department of Mathematics, Evry University 91025 Evry, France E-Mail: [email protected]
Let A be a finite or infinite set of primes. let B be the multiplicative system of all natural numbers which are products, with muliplicity, of primes in A. We consider the P s zeta function associated to B given by ζB(s) = n∈B 1/n . We study this function. This function plays a central role in the multiplicative partition theory. We discuss many important and concrete cases for A. Several known arithmetical functions will be appear. 2010 MSC. Primary 11M06, 11P82.
A study of convolution sums of divisor functions
Abdelmejid Bayad, Nazli Yildiz Ikikardes and Daeyeoul Kim Universit´ed’Evry Val d’Essonne, Balikesir University, NIMS E-Mail:[email protected]; [email protected]; [email protected]
In this talk, we study combinatoric convolution sums, of even indices, involving divisor functions. First, we establish two explicit formulas for certain combinatoric convolution sums of divisor functions derived from Bernoulli and Euler polynomials. Second, as appli- cations, we show several convolution sums of divisor functions expressed by their divisor functions and linear combination of Bernoulli or Euler polynomials. As applications of these identities, we give several concrete interpretations in terms of the procedural modeling method. 2010 MSC. 11B68, 11A05, 11K65. This work was supported by The Research Fund of Balikesir University, Project No: 2014/32. 38
Zagreb indices and coindices of double graphs of certain graph types
Ismail Naci Cangul, Muge Togan, Aysun Yurttas Uludag University, Faculty of Arts and Science, Department of Mathematics Gorukle 16059 Bursa, Turkey E-Mail: [email protected]; [email protected]; [email protected]
Two of the most important topological invariants of graphs called First and second Zagreb indices were defined about 40 years ago as topological graph invariants and they have nice applications in Chemistry. Later, several other versions of these indices were defined in terms of vertex degrees. Here we study double graphs of certain graph types. We give some new formulae for each graph type and also some relations between them. 2010 MSC Primary 05C10, 05C30, Secondary 68R10, 68Uxx
Actuarial Science Education in Mathematics Departments
B. A. Case∗ Department of Mathematics, Florida State University Tallahassee, FL USA Y. M. Guan Department of Mathematics and Actuarial Science Indiana University Northwest Gary, IN USA E-Mail:[email protected]
The mathematical research progress reported in these conference abstracts is impres- sive. This work represents only part of tripartite faculty responsibilities in many uni- versities; there may be expectations of teaching and service in addition to research, and there is growing concern about the employability of students. As a result, a number of mathematicians in the U.S. do most of their teaching and service related to an actu- arial program, finding this an interesting way to work with students and to help their graduates find good employment. Actuarial science is frequently offered to students in 39
U.S. and Canadian mathematics departments and this choice is now available in many universities around the globe. There are challenges involved in initiating and building such a program, but there are good payoffs for the students who are involved: Jobs Rated Almanac and CareerCast in the U.S. frequently classify actuary as the #1 best job. The journal Primus (Taylor and Francis) will devote an edition (late in 2014 or early in 2015) to actuarial science education. A paper accepted for that edition (authors Case, M. Guan, S. Paris) ad- dresses Recruiting and Advising Challenges in Actuarial Science from the viewpoint of increasing the size and effectiveness of a program. In this paper we discuss the content (mathematics, statistics, economics, and finance) supporting an actuarial program, along with challenges in helping students be ready for the profession. Our examples are from universities in the U.S. and China, but we are interested in sharing ideas with those from other countries. In North America, this preparation is heavily influenced by the actuarial professional credentialing societies, and their requirements often derive from various laws and require- ments of governmental agencies. Historically, actuaries in North America, who had often studied pure mathematics topics, were active as contributors to mathematical societies; one of the founders (1894) of what is now the American Mathematical Society (AMS) was a working actuary, and the second president of the AMS was an actuary. A similar relationship carries over today in the USA. At each annual Joint Mathematics Meeting, mathematicians from actuarial science programs at their universities plan a session for interested colleagues. The authors of this paper are part of the group planning those sessions. Their research and degrees are in mathematics, but each is involved in the actuarial program at the university where she is on the mathematics faculty; Guan in- cluded actuarial science in her pre-doctoral study at the School of Mathematical Sciences, Peking University, a decade ago. Related to their own university programs and annual presentations at national meetings, both work with credentialing society representatives and publishers. We hope this experience will be of interest to mathematicians in various university settings. 2010 MSC. 91B30; 97M30; 97U30
Dirichlet problem for higher-order nonlinear complex partial differential equations in an unbounded domain
A. Okay C¸elebi1∗ and Umit¨ Aksoy2 1 Department of Mathematics, Yeditepe University, Istanbul,˙ Turkey 40
E-Mail: [email protected] 2 Department of Mathematics, Atilim University, Ankara, Turkey E-Mail: [email protected]
In this study, we consider nonlinear elliptic equations of higher-order with Dirichlet conditions in an unbounded domain. Firstly, using the integral representation for the solution of the inhomogeneous polyanalytic equation, a class of integral operators is introduced. Then, these operators are used to transform the problem under consideration into an integro-differential system. Finally, existence of the solutions of the boundary value problem is discussed via fixed point theorems. 2010 MSC. Primary 35J60; Secondary 30E25.
On common selectors for a continuum of set-valued maps and its fixed points
Parin Chaipunya1, Yeol Je Cho2, Poom Kumam1 1Department of Mathematics King Mongkut’s University of Technology Thonburi 126 Pracha Uthit Rd., Bangmod, Thung Khru, Bangkok 10140, Thailand 2Department of Mathematics Education and the RINS Gyeongsang National University Chinju, 660-701 Korea
E-Mail: [email protected]
In this talk, we shall present some results governing the existence of a common fixed point for infinitely many set-valued maps. More precisely, we shall investigate on a family ∗ of maps T := {Tα}α∈Λ whose common selector T is uniquely determined and shares its ∗ ∗ T fixed point x = T x with the whole family, i.e., x = T x ∈ α Tαx. 2010 MSC. Primary 54H25; Secondary 47H09. 41
Bilevel vector pseudomonotone equilibrium problems
Jiawei Chen School of Mathematics and Statistics, Southwest University Chongqing 400715, Peoples’ Republic of China E-Mail: [email protected]
This presentation concerns the duality and existence of solutions for a class of bilevel vector pseudomonotone equilibrium problems without involving the information about the solution set of the lower-level equilibrium problem. Firstly, we propose the dual for- mulations of bilevel vector equilibrium problems (shortly, (BVEP)). Secondly, the primal- dual relationships are derived under cone-convexity and weak pseudo-monotonicity as- sumptions. Finally, existence of solutions of (BVEP) are established without involving the information about the solution set of the lower-level problem. 2010 MSC. 49J40; 90C33.
On zeros of the sum of two monotone operators in Hilbert spaces
Sun Young Cho1, Shin Min Kang1 and and Xiaolong Qin2 1Department of Mathematics, Gyeongsang National University Jinju 660-701, Republic of Korea E-Mail: [email protected] and [email protected] 2Department of Mathematics, Hangzhou Normal University Hangzhou 310036, China E-Mail: [email protected]
In this talk, we shall investigate a splitting process for two monotone operators and consider the problem of finding an element in the zero point set of the sum of two operators. 2010 MSC. 47H05, 47H09, 47J25. 42
Approximating fixed points of nonlinear mappings
Yeol Je Cho Department of Mathematics Education Gyeongsang National University Jinju 660-701, Korea E-mail: [email protected] (Yeol Je Cho)
In this paper, as a survey of recent results on fixed point theory, (1) first, we introduce some kinds of nonlinear mappings in Hilbert spaces and Banach spaces and their relations and examples. (2) second, we give some open problems. (3) finally, we prove some weak and strong convergence theorems for Moudafi’s itera- tive scheme including (a, b)-monotone and nonexpansive mappings in Hilbert spaces and give some examples to illustrate our main results. The results in this paper improve and extend the recent results of Iemoto and Takahashi, Lin and Wang and some others.
Reduction method for a class of the semilinear elliptic systems
Q-Heung Choi Department of Mathematics Education, Inha University Incheon 402-751, Republic of Korea E-Mail: [email protected]
We get a theorem which shows the existence of at least three nontrivial solutions for a class of the systems of the elliptic equations with some nonlinearity and boundary con- dition. We obtain this result by approaching the variational method, the critical point theory and the topological method. 43
Several recent results regarding the Riemann zeta function ζ(s)
Junesang Choi Department of Mathematics, Dongguk University Gyeongju 780-714, Republic of Korea E-Mail: [email protected]
Ever since Euler first evaluated ζ(2) and ζ(2m), numerous interesting solutions of the problem of evaluating the ζ(2m)(m ∈ N) have appeared in the mathematical literature. Until now no simple formula analogous to the evaluation of ζ(2m)(m ∈ N) is known for ζ(2m + 1) (m ∈ N) or even for any special case such as ζ(3). Instead, various rapidly converging series for ζ(2m + 1) have been developed by many authors. Here, using Fourier series, we give a recurrence formula for rapidly converging series for ζ(2m + 1). In addition, using Fourier series and recalling some indefinite integral formulas, we also give recurrence formulas for evaluations of β(2m + 1) and ζ(2m)(m ∈ N), which have been treated in earlier works. We further present a double inequality approximating ζ(2m + 1) by a more rapidly convergent series. 2010 MSC. Primary 11M06, 42A16; Secondary 11B68, 11Y60.
H H The incomplete Srivastava’s triple hypergeometric functions γB and ΓB
Junesang Choi1, Rakesh K. Parmar2∗ and Purnima Chopra3 1Department of Mathematics, Dongguk University, Gyeongju 780-714, Republic of Korea E-Mail: [email protected] 2Department of Mathematics, Government College of Engineering and Technology, Bikaner-334004, Rajasthan State, India E-Mail: [email protected] 3Department of Mathematics, Marudhar Engineering College, Bikaner-334001 , Rajasthan State, India E-Mail: [email protected] 44
In a recent paper, Srivastava et al. [2] introduced the incomplete Pochhammer symbols by means of the incomplete gamma functions γ(s, x) and Γ(s, x) ,and defined incomplete hypergeometric functions and investigated a number of interesting fundamental proper- ties and characteristics.Further, C¸etinkaya [1] introduced the incomplete second Appell hypergeometric functions and studied many interesting fundamental properties and char- acteristics. In this paper,we introduce the incomplete Srivastava’s triple hypergeometric H H functions γB and ΓB based upon these incomplete Pochhammer symbols and investi- gate certain properties , for example, their various integral representations,derivative formula,reduction formula and recurrence relation.Various (known or new) special cases and consequences of the results presented in this article are considered. 2010 MSC. Primary 33B15, 33B20, 33C05, 33C15, 33C20; Secondary 33B99, 33C99, 60B99.
References [1] A. C¸etinkaya, The incomplete second Appell hypergeometric functions, Appl. Math. Comput. 219 (2013), 8332–8337. [2] H. M. Srivastava, M. A. Chaudhry and R. P. Agarwal, The incomplete Pochhammer symbols and their applications to hypergeometric and related functions, Integral Transforms Spec. Funct. 23 (2012), 659–683.
Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators in non-compact settings
Mohammad S. R. Chowdhury∗ and Yeol Je Cho† Department of Mathematics University of Management and Technology (UMT) Lahore-54770, Pakistan
E-Mail: [email protected] ∗; yjchomathgnu.ac.kr†
A new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo- monotone type II operators in non-compact settings has been introduced in locally convex Hausdorff topological vector spaces. Some existence results of solutions for the above GBQVI have been obtained. 45
In 1985, K.C. Border introduced the concept of escaping sequences in the book: ”Fixed Point Theorems with Applications to Economics and Game Theory”. Using this concept of escaping sequences, we shall obtain our results on GBQVI for quasi-pseudo-monotone type II operators in non-compact settings. But the main tools that we shall apply in obtaining our results are Chowdhury and Tan’s result on generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets. As applica- tion, an existence theorem on generalized bi-complementarity problem for quasi-pseudo- monotone type II operators is given in non-compact settings. 2010 MSC. Primary 47J40, 49H; Secondary 54C
Generalized quasi-variational inequalities for pseudo-monotone type III and strongly pseudo-monotone type III operators on non-compact sets
Mohammad S. R. Chowdhury∗ and Yeol J Cho† Department of Mathematics University of Management and Technology (UMT) Lahore-54770, Pakistan Department of Mathematics Education and RINS Gyeongsang National University Jinju 660-701, Korea
E-Mail: [email protected] ∗; yjchomathgnu.ac.kr †
In this paper, the authors prove some existence results of solutions for a new class of generalized quasi-variational inequalities (GQVI) for pseudo-monotone type III operators and strongly pseudo-monotone type III operators defined on non-compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GQVI for pseudo-monotone type III and strongly pseudo- monotone type III operators, we shall use Chowdhury and Tan’s generalized version of Ky Fan’s minimax inequality as the main tool. 2010 MSC. Primary 47J40, 49H; Secondary 54C 46
Integral–valued polynomials associated with finite trigonometric sums
Djurdje Cvijovi´c Atomic Physics Laboratory, VinˇcaInstitute of Nuclear Sciences P.O. Box 522, 11001 Belgrade, Serbia E-Mail: [email protected]
A polynomial Pn(x) is said to be integral-valued if Pn(x) is an integer whenever x is an integer. These polynomials, also known as numerical polynomials, were first introduced by P´olya (1915) and have been extensively studied in the meantime. In recent years, it has been shown by several authors that summation of some finite trigonometric sums gives rise to integral-valued polynomials. Herein, two novel families of integral-valued polynomials are described in full detail. They are related to each other by the bino- mial transformation and associated with certain cotangent and cosecant sums. Further, several already known families of numerical polynomials are demonstrated to be spe- cial cases of our results. In addition, it appears to be possible that here used approach could give all, known and unknown, integral-valued polynomials associated with finite trigonometric sums. 2010 MSC. Primary 11B83, 26C05; Secondary 11B99, 26C99.
Sharper uncertainty principle in signal analysis
Pei Dang Department of General Education, Macau University of Science and Technology Macao, China E-Mail: [email protected]
The work strengthens the result established by L. Cohen on uncertainty principle involving phase derivative. We propose stronger uncertainty principles not only in the classical setting for Fourier transform, but also for self-adjoint operators and Linear canonical transform. We also deduce the conditions that give rise to the equal relation of the uncertainty principle. 47
On the (p,q)-th relative order oriented growth properties of entire functions
Sanjib Kumar Datta Associate Professor and Head Department of Mathematics, University of Kalyani P.O.- Kalyani, Dist-Nadia, PIN-741235, West Bengal, India. E-Mail: sanjib kr [email protected]
The relative order of growth gives a quantitative assessment of how different func- tions scale each other and until what extent they are self-similar in growth. For any two positive integers p and q, here we wish to introduce an alternative definition of relative (p, q)-th order which improves the earlier definition of relative (p, q)-th order as intro- duced by Lahiri and Banerjee {cf. B. K. Lahiri and D. Banerjee : Entire functions of relative order (p, q) , Soochow Journal of Mathematics, Vol. 31, No. 4 (2005), pp. 497- 513}. Also we discuss some growth rates of entire functions on the basis of the improved definition of relative (p, q)-th order with respect to another entire function and extend some earlier concepts as given by Lahiri and Banerjee {cf. B. K. Lahiri and D. Banerjee : Entire functions of relative order (p, q) , Soochow Journal of Mathematics, Vol. 31, No. 4 (2005), pp. 497-513}, providing some examples of entire functions whose growth rate can accordingly be studied. 2010 MSC. Primary 30D35, 30D30; Secondary 30D20.
The shrinking projection method for solving the split feasibility, fixed point and system of equilibrium problems
Jitsupa Deepho and Poom Kumam Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) 126 Pracha Uthit Rd., Bang Mod, Thrung Khru, Bangkok 10140, Thailand E-Mail: [email protected]; [email protected]
The split feasibility problem (SFP) (Censor and Elving 1994 Numer. Algorithms 8 221-39) is to find a point x∗ with the property that x∗ ∈ C and Ax∗ ∈ Q, where C and Q 48 are the nonempty closed convex subsets of the real Hilbert space H1 and H2, respectively, and A is a bounded linear operator from H1 to H2. The SFP models inverse problems arising from phase retrieval problems (Censor and Elfving 1994 Numer. Algorithms 8 221-39) and in the intensity-modulated radiation therapy (Censor et al 2005 Inverse Problems 21 2071-84). In this paper, we suggest a hybrid extragradient method for finding a common element of the set of fixed point sets of an infinite family of nonexpansive mappings, the solution set of the split feasibility problem (SFP) and system of equilibrium problems in real Hilbert spaces. 2010 MSC. Primary 47H10, 47J25, 47J40; Secondary 90C33.
Control of the systems subjected by interval perturbation
Dmitry V. Dolgy Hanrimwon, Kwangwoon University Seoul 139-701, Republic of Korea
E-Mail: d−[email protected]
The new method of control of the systems subjected perturbations is suggested. It based on approximation of terminal set by cubes or parallelepiped. It is obtained that the problem of control is reduced to the linear problem. 2010 MSC. Primary 11A50.
The condition of small girth for the moduli of curves on Finsler spaces
Yuri Dymchenko Department of Mathematics, Far East Federal University Vladivostok, Russia 49
E-Mail: [email protected]
Let G ⊂ Rn — domain in the Finsler space with the distance function F (x, dx). There is proved the equivalence of two conditions for compact set E ⊂ G. The first condition is the property of set to be a NCp,F -set, i.e. for all closet disjoint sets E0, E1 ⊂ G it holds the equality of two capacities: Cp,F (E0,E1,G) = Cp,F (E0,E1,G \ E). The second condition may be formulated as follows. We consider the family Γ of disjoint curves γ such that their union is filled a some domain G0 ⊂ G, and ρ is locally bounded Borel function on G. Then for all ε > 0, almost all γ ∈ Γ there exist collection of curves γ0, continuumγ ˜ ⊂ γ ∪ γ0 which does not meet E, joins the same two points as the curve γ and R ρF (x, dx) < ε. γ0 2010 MSC. 31B15
Existence and iterative approximation of solutions of generalized mixed vector equilibrium problems in a Banach space
Mohammad Farid Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India E-Mail: [email protected]
In this paper, we introduce an iterative schemes for finding a common solution of gen- eralized mixed vector equilibrium problem and fixed point problems in Banach space. We study the strong convergence of the sequences generated by the proposed iterative schemes. The results presented in this paper are the supplement, extension and gener- alization of the previously known results in this area. 2010 MSC. 49J30, 47H10, 47H17, 90C99. 50
Several expansion formulas involving the generalized Hurwitz-Lerch zeta ∗ function Φµ(z, s, a) with applications to Apostol-type polynomials
S´ebastienGaboury Department of Mathematics and Computer Science, University of Qu´ebec at Chicoutimi Chicoutimi, Qu´ebec G7H 2B1, Canada E-Mail: [email protected]
The object of this talk is to present some new expansion formulas for the generalized ∗ Hurwitz-Lerch zeta function Φµ(z, s, a) obtained recently by Gaboury and Bayad (S. Gaboury, A. Bayad, Further expansion formulas for a class of generalized Hurwitz-Lerch zeta function obtained by means of a new Leibniz rule for fractional derivatives, Preprint 2013) and by Gaboury (S. Gaboury, Some relations involving generalized Hurwitz-Lerch zeta function obtained by means of fractional derivatives with applications to Apostol- type polynomials, Adv. Difference Equations 361 (2013), 1–13). These expansion for- mulas was obtained by making use of some important fractional calculus theorems. Ex- plicit series representations for the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi and Apostol-Frobenius-Euler polynomials of higher order are also considered. Finally, some further expansion formulas investigated recently by Srivastava et al. (H. M. Sri- vastava, S. Gaboury and A. Bayad, Expansion formulas for an extended Hurwitz-Lerch zeta function obtained via fractional calculus, Preprint 2014) are also discussed. 2010 MSC. Primary 26A33, 11M35 ; Secondary 33C05, 11B68.
Stability of functional equations In non-Archimedean spaces
M. B. Ghaemi and H. Majani School of Mathematics Iran University of Science and Technology Tehran, Iran E-Mail: [email protected]
We prove the generalized Hyers–Ulam–Rassias stability for a system of functional equations, called system of linear and nonlinear functional equations in non-Archimedean normed spaces and Menger probabilistic non-Archimedean normed spaces. 51
2010 MSC. Primary 39B82, Secondary 39B52.
Extreme points and support points associated with n univalent subordination chains in C
Hidetaka Hamada Faculty of Engineering, Kyushu Sangyo University Fukuoka 813-8503, Japan E-Mail: [email protected]
Let S0(Bn) denote the family of mappings which have parametric representation on n n 0 n the Euclidean unit ball B in C , i.e. f ∈ S (B ) if and only if there exists a (normalized) −t n Loewner chain f(z, t) such that f = f(·, 0) and {e f(·, t)}t≥0 is a normal family on B . In this talk, We consider extreme points and support points of S0(Bn). We also consider extremal problems related to bounded mappings in S0(Bn). 2010 MSC. Primary 32H02; Secondary 30C45.
Decomposition formulae for generalized hypergeometric functions with the Gauss-Kummer identity
Naoya Hayashi Josho Gakuen High School 5-16-1, Omiya, Asahi-ku, Osaka, Osaka, 577-8585, Japan E-Mail: [email protected]
Yutaka Matsui∗ Department of Mathematics, Kinki University 3-4-1, Kowakae, Higashi-Osaka, Osaka, 577-8502, Japan E-Mail: [email protected] 52
The generalized hypergeometric function ∞ n α1, α2, . . . , αp X (α1)n(α2)n ··· (αp)n x (1) pFq ; x = β1, β2, . . . , βq (β ) (β ) ··· (β ) n! n=0 1 n 2 n q n plays an important role in not only mathematics but also applied mathematics, physics, engineering and so on, and has been studying by many mathematicians. In the theory of special functions, it is important to study some relations among such important spe- cial functions. A decomposition formula for a hypergeometric function is the one which describes the hypergeometric function with a summation of other hypergeometric func- tions, such as (2) below. The aim of this talk is to introduce our study [2] for similar type of decomposition formulae to Choi-Hasanov’s ones [1]. An example of our main results is the following: ∞ (α − β ) (α ) α1, α2 −α1 X 2 1 i 1 1 α1 + 1, α2 + 1, i + 1 (2) 2F1 ; x = (1 − x) + x3F2 ; x . β1 (α + 1) α2 + i + 1, 2 i=1 2 i Note that although we focus mainly on the generalized hypergeometric functions we could also obtain a lot of decomposition formulae for various special functions by our methods. 2010 MSC. Primary 33C20, 33C05, 30B10
References
[1] J.Choi and A.Hasanov, Certain decomposition formulas of generalized hypergeometric functions pFq and some formulas of an analytic continuation of the Clausen function 3F2, Commun. Korean Math. Soc. 27(2012), 107-116. [2] N. Hayashi and Y. Matsui, Decomposition formulae for generalized hypergeometric functions with the Gauss-Kummer identity, Commun. Korean Math. Soc. 29(2014), 97-108.
Growth and distortion theorems on a homogeneous unit ball
Tatsuhiro Honda Hiroshima Institute of Technology, Hiroshima 731-5193, Japan E-Mail: [email protected]
We recall the growth and distortion theorems on the open unit disc U = {x ∈ C; |x| < 1} in the complex plane C. 53
[Growth Theorem] If f : U −→ C be a univalent holomorphic function on U in df with f(0) = 0, (0) = f 0(0) = 1, then for z ∈ U, C dz |z| |z| (3) ≤ |f(z)| ≤ . (1 + |z|)2 (1 − |z|)2 Moreover, if f is convex, then |z| |z| (4) ≤ |f(z)| ≤ . 1 + |z| 1 − |z|
[Distortion Theorem] If f : U −→ C be a univalent holomorphic function on U 0 in C with f(0) = 0, f (0) = 1, then for z ∈ U, 1 − |z| 1 + |z| (5) ≤ |f 0(z)| ≤ . (1 + |z|)3 (1 − |z|)3 Moreover, if f is convex, then 1 1 (6) ≤ |f 0(z)| ≤ , (1 + |z|)2 (1 − |z|)2
Various growth and distortion theorems for univalent functions have been studied. The object of this talk is to generalize the growth and distortion theorems for holo- morphic mappings on a homogeneous unit ball of a complex Banach space. 2010 MSC. Primary 32M15, 32A30; Secondary 31C10.
Chordal Loewner chains with quasiconformal extensions
Ikkei Hotta Department of Mathematics, Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan E-Mail: [email protected]
In 1972 Becker showed that if a Herglotz function p associated with a classical radial Loewner chain (ft) satisfies |(1−p(z, t))/(1+p(z, t))| ≤ k for all z lies in the unit disk and almost every t ≥ 0, then the initial link f0 of the Loewner chain has a k-quasiconformal 54 extension to the complex plane. In this talk the chordal variant of Becker’s quasicon- formal extension criterion is introduced in the general setting of the theory of evolution families and Herglotz functions. It is worth to mention that our results derive some relations of Herglotz functions and the behavior of the (decreasing) Loewner range. The results are based on joint work with Dr. Pavel Gumenyuk. 2010 MSC. Primary 30C62, Secondary 30C35, 30D05.
The (S, {2})-Iwasawa theory
Su Hu Department of Mathematics and Statistics, McGill University 805 Sherbrooke St. West, Montreal, Quebec, H3A 2K6, Canada E-Mail: [email protected]
Iwasawa made the fundamental discovery that there is a close connection between the ideal class groups of Zp-extensions of cyclotomic fields and the p-adic analogue of Riemann’s zeta functions ∞ X 1 ζ(s) = . ns n=1 In this talk, we show that there may also exist a parallel Iwasawa’s theory corresponding to the p-adic analogue of Euler’s deformation of zeta functions
∞ X (−1)n−1 φ(s) = . ns n=1 This is a joint work with Professor Min-Soo Kim. 2010 MSC. Primary 11R23; Secondary 11S40, 11S80.
On q-difference Riccati equation and q-Gamma function 55
Zhi-Bo Huang School of Mathematical Sciences, South China Normal University Guangzhou 510631, P. R. China E-Mail: [email protected]
In this paper, we consider a certain type of q-difference Riccati equation in the complex plane, and obtain the transformations between the q-difference Riccati equation and second order linear q-difference equation, the representations and value distribution of meromorphic solutions of q−difference Riccati equation. In particular, by constructing a crucial M¨obiustransformation, we find that the meromorphic solutions of q-difference Riccati equation are concerned with the q-Gamma function when q ∈ C such that 0 < |q| < 1. 2010 MSC. Primary 30D35, 39B32; Secondary 34M05.
Bilinear pairings and their applications
Andrea Huszti Faculty of Informatics, University of Debrecen Debrecen, Hungary E-Mail: [email protected]
Bilinear pairings, namely Weil pairing and Tate pairing of algebraic curves were used in cryptography for MOV attack using Weil pairing and FR attack using Tate pairing. These attacks reduce the discrete logarithm problem on some elliptic or hyperelliptic curves to the discrete logarithm problem in a finite field. Bilinear pairings have recently been used to design cryptographic protocols, since as a consequence new constructions of primitives appeared. These primitives either cannot be built using other techniques, or they can be created via traditional methods, but pairings provide improved functionality. Here, we show how these new primitives can be applied in e-commerce to accomplish necessary security requirements reducing both financial and computational costs. 56
On the extended Hecke groups
Sebahattin Ikikardes and Recep Sahin Department of Mathematics, Balikesir University Balikesir 10145, Turkey E-Mail: [email protected],[email protected]
In this talk, we introduce extended Hecke groups and their subgroups. Also, we give the relationships with the other special groups of these groups. 2010 MSC. Primary 20H10; Secondary 11F06.
Integrals containing Laguerre type polynomials and Bessel functions
Shilpi Jain Department of Mathematics Poornima College of Engineering Jaipur-302022, India E-Mail: [email protected]
In the present paper, we aim to establish the certain integrals involving unified four parameter Laguerre polynomials and the Bessel-type functions. On account of the most general nature of the functions involved herein, our main findings are capable of yielding a large number of new, interesting and useful integrals, expansion formulae involving the Laguerre polynomials and Bessel function as their special cases. 2010 MSC. 65A05; 33C45; 44A15.
q-Changhee and Boole polynomials 57
Yu Seon Jang, Taekyun Kim, Hyuck-In Kwon and Jong-Jin Seo Department of Mathematics, Kwangwoon University Seoul 139-701, Republic of Korea
E-Mail: [email protected], [email protected], sora−@naver.com, [email protected]
Boole polynomials play an important role in the area of number theory, algebra and umbral calculus. Recently, D. S. Kim and T. Kim investigated some properties of Boole and Changhee polynomials and considered Witt-type formulas for the Boole numbers and polynomials (see Integral Transforms and Special Functions 2014). In this paper, we consider the q-extensions of Changhee and Boole polynomials. From those polyno- mials, we derive some new and interesting identities and properties related to special polynomials. 2010 MSC. Primary 11B68, 11S80.
Some results regarding the Schwarz lemma about the boundary fixed points
Moonja Jeong Department of Mathematics, The University of Suwon Gyeonggido 445-743, Republic of Korea E-Mail: [email protected]
The classical Schwarz lemma deals with the size of the value of holomorphic maps defined on the unit disc at any point when the origin is fixed. Equality in the classi- cal Schwarz lemma holds only for rotation map. Moreover, it is known that the only holomorphic self map of the unit disc having another fixed point except the origin is the identity map. We consider holomorphic maps having fixed points only on the boundary of the unit disc and find examples of them and find some properties. 2010 MSC. Primary 30C80; Secondary 30C35. 58
On some compatible type mappings in metric space
Kanhaiya Jha Department of Mathematical Sciences, School of Science, Kathmandu University, POBox Number 6250, Kathmandu, Nepal E-Mail: [email protected]; [email protected]
The study of common fixed point of mappings in a metric space and its subspaces satisfying certain contractive conditions has been at the center of vigorous research ac- tivities. Also, with the advent of notion of compatible mappings introduced by G. Jungck in 1986, it has centered on the study of compatible mappings and its weaker forms. On the other hand, the study of non-compatible maps is also equally interesting. The pur- pose of the presentation is to discuss the new notion of K-compatible mappings which is independent of some existing compatible type mappings and some common fixed point results. 2010 MSC. Primary 47H10, Secondary 54H25.
Special lightlike hypersurfaces of indefinite Kaehler manifolds
Dae Ho Jin Department of Mathematics, Dongguk University Gyeongju 780-714, Republic of Korea E-Mail: [email protected]
In this paper, we define three types of lightlike hypersurfaces of an indefinite Kaehler manifold, which are called Hopf, recurrent and Lie recurrent lightlike hypersurfaces. After that we provide several new results on such special lightlike hypersurfaces M of an indefinite Kaehler manifold M¯ or an indefinite almost complex space form M¯ (c). 2010 MSC. 53C25, 53C40, 53C50. 59
A hybrid iterative algorithm for inverse-strongly monotone mappings and strictly pseudocontractive mappings
Jong Soo Jung Department of Mathematics, Dong-A University Busan 604-714, Republic of Korea E-Mail: [email protected]
In this talk, we introduce a new hybrid iterative algorithm for finding a common element of the set of solutions of variational inequality problem for an inverse-strongly monotone mapping and the set of fixed points of a strictly pseudo-contractive mapping in a Hilbert space and then establish strong convergence of the sequence generated by the proposed iterative algorithm to a common element of the above two sets under suitable control conditions, which is a solution of a certain variational inequality. 2010 MSC. 47H06, 47H09, 47H10, 47J20, 49J40, 47J25, 47J05.
Four solutions for the Hamiltonian system
Tacksun Jung Department of Mathematics, Kunsan National University Kunsan 573-701, Republic of Korea E-Mail: [email protected]
We get a theorem which shows the existence of at least four 2π−periodic weak so- lutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We obtain this result by using the variational method, the critical point theory induced from the limit relative category theory. 60
On the problem of decomposition and composition of normal ring open sets
Tatiana Kalmykova and Vladimir Shlyk∗ Department of Algebra, Geometry and Mathematicfl Analysis, Far East Federal University Vladivostok, Russia E-Mail: [email protected]; [email protected]
There is an extensive literature devoted to investigations of the properties of normal domains (normal domains in the Gr¨otzsch sense or minimal domains in the Koebe sense). Here, using the method of extremal metric in Fugledes sense we give a solution of the problem decomposition and composition of p-normal ring open sets, 1 < p < ∞, of the n-dimensional Euclidean space Rn, n ≥ 2. 2010 MSC. 31B15
Pythagorean means and differential subordinations
Stanislawa Kanas Faculty of Mathematics and Natural Sciences University of Rzeszow, Poland E-Mail: [email protected]
The three classical means; arithmetic, geometric and harmonic mean were studied with proportions by Pythagoreans and later generations of Greek mathematicians. An arithmetic and geometric means were frequently studied in Geometric Functions Theory; in particular in the theory of differential subordinations. The aim of a study is the differential subordination involving harmonic means of the expressions p(z), p(z)+zp0(z), zp0(z) and p(z)+ p(z) when p is an analytic function in the unit disk, such that p(0) = 1, p(z) 6≡ 1. Another example is the differential subordination with the expression combined by arithmetic and geometric means:
zp0(z)µ α[p(z)]δ + (1 − α) p(z) + ≺ ϕ(z), (p(0) = ϕ(0) = 1, |z| < 1), p(z) 61 where δ, µ and α are real numbers such that δ, µ ∈ h1, 2i, α ∈ h0, 1i. For δ ∈ h1, 2i, µ ∈ h0, 1i, α ∈ h0, 1i we also study the differential subordination
zp0(z)1−µ α[p(z)]δ + (1 − α)[p(z)]µ p(z) + ≺ ϕ(z), (p(0) = ϕ(0) = 1, |z| < 1). p(z)
Several applications of the studied subordination in the theory of analytic functions are given. This is joint work with my students: Oana Crisan and Andreea Helena Tudor, Cluj- Napoca University, Romania, E-Mails: [email protected], tudor andreea [email protected]. 2010 Mathematics Subject Classification: Primary 30C45; Secondary 30C55, 34M99.
A research of symmetry on the twisted Genocchi polynomials with weak weight α
J. Y. Kang∗ and C. S. Ryoo Department of Mathematics, Hannam University Daejeon 306-791, Republic of Korea E-Mail: [email protected]
The main purpose of this paper is to study an identities of symmetry for the twisted Genocchi polynomials with weak weight α. We investigate some relations between the power sum polynomials and twisted Genocchi polynomials with weak weight α by using p-adic q-integral on Zp. We also figure out the symmetric properties of these polyno- mials considering zeta function. In addition, we find the symmetric identities of those polynomials of higher order m in complex plane. 2010 MSC. Primary 11B68, 42A16; Secondary 11S40, 11S80.
On some applications of special functions to the investigation of boundary-value problems for PDEs 62
E. T. Karimov Institute of Mathematics, National University of Uzbekistan Tashkent 100125, Uzbekistan E-Mail: [email protected]
It is well-known that fundamental solutions of most partial differential equations con- tain special functions. Therefore, further investigations of these equations depend on certain properties of appropriate special functions. Precisely, in this talk we discuss applications of hypergeometric functions of the Lauricella, Appel and Gauss at study- ing main boundary-value problems for 3-D elliptic equations with singular coefficients. Moreover, we as well, consider some applications of properties of the Mittag-Leffler, Wright functions to the studying local and non-local boundary-value problems for mixed parabolic-hyperbolic equations with the Caputo fractional order differential operator. 2010 MSC. Primary 35J25, 35M10; Secondary 33C05, 33E12.
Distributional G-function and representations of generalized hypergeometric functions
Dmitrii Karp Far Eastern Federal University Vladivostok, Russian Federation E-Mail: [email protected]
Integral representations of generalized hypergeometric functions q+1Fq(α; A; B; z) (Gauss type) and qFq(A; B; z) (Kummer type), where A = (a1, . . . , aq), B = (b1, . . . , bq), de- Pq pend on the parametric excess ψ = i=1(bi − ai). It is known that for ψ > 0 these representations for the Gauss and Kummer type functions are generalized Stieltjes and Laplace transforms of summable functions, respectively. We demonstrated that under majorization condition B ≺W A one gets generalized Stieltjes and Laplace transforms of a nonnegative measure. This measure has a density if and only if ψ > 0. In the talk we discuss the representing measure for ψ = 0 and possible representations for ψ < 0. In the latter case we show that one can represent the generalized hypergeometric functions by an action of a distribution expressed in terms of Meijer G-function on the generalized 63
Stieltjes kernel (1 − zt)−α (for the Gauss type functions) or Laplace kernel exp(−zt) (for the Kummer type function). Various consequences of these results will also be given. The talk reflects the results of the joint work with J.L.L´opez (Universidad P´ublicade Navarra, Spain). 2010 MSC. Primary 33C20, 33C60
Modified mann iterative for variational inequality problem and common fixed point problems of nonexpansive mappings and nonexpansive semigroups in q-uniformly smooth Banach spaces
Phayap Katchang Division of Mathematics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Tak (RMUTL Tak), Tak 63000, Thailand E-Mail: [email protected]
In this paper is to introduce a new iterative scheme for finding common element of the set of common fixed points of an infinite family of nonexpansive mappings and nonexpansive semigroup mapping and the solution of the variational inequality problem for an inverse-strongly accretive mapping by using the modified Mann iterative method and obtain some strong convergence theorem in a q-uniformly smooth Banach spaces under some parameters controlling conditions. The methods in the paper are novel and different from those in the early and recent literature. Our results extend and improve the recent results in some references. 2010 MSC. Primary 47H09, 47H10, 47H20.
Existence of at least three solution for equations N involving nonhomogeneous operators of p-Laplace type in R
Yun-Ho Kim and Eun Bee Choi∗ 64
Department of Mathematics Education, Sangmyung University Seoul 110-743, Republic of Korea E-Mail: [email protected]; [email protected]∗
In this talk, we are concerned with the following elliptic equations N −div(ϕ(x, ∇u)) = λf(x, u) + θg(x, u) in R , p−2 N where the function ϕ(x, v) is of type |v| v and f, g : R × R → R which satisfy a Carath´eodory condition. The main purpose of this talk is to establish the existence of at least three weak solutions which are based on two recent three critical point theory due to Ricceri. Moreover we determine precisely the intervals of λ’s for which the above problem with θ = 0 possesses either only the trivial solution or at least two nontrivial solutions by using eigenvalue problem associated with the p-Laplacian. 2010 MSC. Primary 35D30, 58E05; Secondary 35J62.
Global Bifurcation result for a class of equations involving p(x)-Laplace type
Yun-Ho Kim and Byung-Hoon Hwang∗ Department of Mathematics Education, Sangmyung University Seoul 110-743, Republic of Korea Department of Mathematics, Sungkyunkwan University Suwon 440-746, Republic of Korea E-Mail: [email protected], [email protected]∗
We are concerned with the following nonlinear problem −div(ψ(x, ∇u)) = µ|u|p(x)−2u + f(λ, x, u, ∇u) in Ω subject to Dirichlet boundary conditions, provided that µ is not an eigenvalue of the N p(x)-Laplacian. Here Ω is a bounded domain in R with Lipschitz boundary ∂Ω, p : p(x)−2 N N Ω → (1, ∞) is continuous, ψ(x, t) is of type |t| , ψ(x, ·): R → R is not necessarily N positively homogeneous or odd and f : R × Ω × R × R → R satisfies a Carath´eodory condition. To our best of our acknowledge, we know that the fact that the principal eigenvalue for p(x)-Laplacian is isolated plays a key role in obtaining the bifurcation result from the principal eigenvalue. However unlike the p-Laplacian case, under some 65 conditions on p(x), the infimum of all eigenvalues for the p(x)-Laplacian might be zero and so if there exists a principal eigenvalue µ∗, then this is not isolated because µ∗ is the infimum of all eigenvalues. Thus we cannot investigate the existence of global branches bifurcating from the principal eigenvalue of the p(x)-Laplacian. However, V¨ath introduced another new approach to establish the existence of a global branch of solutions for nonlinear equations involving the p-Laplacian. Based on the work of V¨ath,in this talk we observe the existence of an unbounded branch of the set of solutions for nonlinear equations of p(x)-Laplace type, by applying a bifurcation result for nonlinear operator equations. MSC. 35B32; 35D30; 35J60; 35P30; 37K50; 46E35; 47J10.
Existence and multiplicity of solutions for equations N involving nonhomogeneous operators of p-Laplace type in R
Yun-Ho Kim and Ji Soo Lee∗ Department of Mathematics Education, Sangmyung University Seoul 110-743, Republic of Korea E-Mail: [email protected]; [email protected]∗
In this talk, we discuss the following elliptic equations
N −div(ϕ(x, ∇u)) = λf(x, u) in R ,
where the function ϕ(x, v) is of type |v|p−2v with p > 1 is a real constant and f : N R × R → R satisfies a Carath´eodory condition. We show the existence of at least one nontrivial weak solution, and under suitable assumptions, infinitely many solutions for the problem above by using Mountain pass theorem and Fountain theorem. Also, we prove that the existence of at least two distinct nontrivial critical points under the appreciate assumptions. 2010 MSC. Primary 35D30, 35J92; Secondary 35J60. 66
Existence of solutions for a Neumann problem involving nonhomogeneous operators of the p(x)-Laplace type
Yun-Ho Kim and Kisoeb Park∗ Department of Mathematics Education, Sangmyung University Seoul 110-743, Republic of Korea Department of Mathematics, Sungkyunkwan University Suwon 440-746, Republic of Korea∗ E-Mail: [email protected]; [email protected]∗
In this talk, we are concerned with the nonlinear elliptic equations of the p(x)- Laplacian type ( −div(a(x, ∇u)) + |u|p(x)−2u = λf(x, u) + θg(x, u) in Ω ∂u ∂n = 0 in ∂Ω, which is subject to Neumann boundary condition, where the function a(x, v) is of type p(x)−2 |v| v with continuous function p : Ω → (1, ∞) and f, g :Ω × R → R satisfies a Carath´eodory condition. The main purpose of this talk is to establish the existence of at least three solutions for the above problem by applying recent three-critical-points theorems due to Ricceri. 2010 MSC. Primary 35D30, 58E05; Secondary 35J62.
N Multiple solutions for the p(x)-Laplace type operator in R
Yun-Ho Kim and Seung Dae Lee∗ Department of Mathematics Education, Sangmyung University Seoul 110-743, Republic of Korea E-Mail: [email protected], [email protected]∗
In this talk, we are concerned with the nonlinear elliptic equations of the p(x)- Laplacian type N −div(ϕ(x, ∇u)) = λf(x, u) + θg(x, u) in R , 67
p(x)−2 N where the function ϕ(x, v) is of type |v| v with continuous function p : R → (1, ∞) N and f, g : R × R → R satisfy a Carath´eodory condition. The main aim of this talk is to establish the existence of at least three solutions for the above problem as the applications of two recent three-critical-points theorems introduced by Ricceri. In addition, by using eigenvalue problem associated with the p(x)-Laplacian, we show the existence of at least two nontrivial critical points of the above equation with θ = 0 for sufficiently large λ. 2010 MSC. Primary 35D30, 58E05; Secondary 35J62.
Generating fractional partial differential equations with variable coefficients via convolutions
A. Kılı¸cman Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia E-Mail: [email protected]
The fractional partial differential equations appeared in many fields of engineering and science, including fractals theory, statistics, fluid flow, control theory,biology, chem- istry, diffusion, probability, and potential theory. Further, singular partial differential equations of fractional order, as generalizations of classical singular partial differential equations of integer order, are increasingly used to model the problems in physics and engineering. Recently, considerable attention has been given to the solution of singu- lar partial differential equations of fractional order. For the solutions there are several methods for solving singular partial differential equations.
In this paper, we are concerned with the singular partial differential equations of fractional order (FSPDEs). Integral transform methods are used to solve this type of equations. Further by using the differential operators with constant coefficients, we generate fractional partial differential equations with variable coefficients. Later the convergence analysis as well as the relationship between the solutions are discussed. The analysis is also used to estimate truncated errors for approximate series solution. The existence of the classical as well as weak solutions and the link between them before and after convolution operation is also studied. 2010 MSC. Primary 35L05; Secondary 44A35. 68
Hyers–Ulam stability of homomorphisms and derivations on normed Lie triple systems
Hark-Mahn Kim and Juri Lee∗ Department of Mathematics, Chungnam National University Daejeon, 305-764, Republic of Korea E-Mail: [email protected]; [email protected]
In this talk, we study the generalized Hyers–Ulam stability of homomorphisms and derivations on normed Lie triple systems for the following generalized Cauchy–Jensen additive equation
Pp Pd p d s j=1 xj + t j=1 yj X X r f = s f(x ) + t f(y ) 0 r j j 0 j=1 j=1
where r0, s, t are nonzero real numbers. As results, we generalize some stability results concerning this equation. 2010 MSC. Primary 39B82, 16W25, 17A40.
Generalized Hyers–Ulam Stability of Functional Inequalities
Hark-Mahn Kim Department of Mathematics, Chungnam National University, 79 Daehangno, Yuseong-gu, Daejeon 305-764, Republic of Korea E-Mail: [email protected]
Eunyoung Son∗ Department of Mathematics, Chungnam National University, 79 Daehangno, Yuseong-gu, Daejeon 305-764, Republic of Korea E-Mail: [email protected] 69
In this talk, we prove the general solution of the following cubic functional inequality
kf(2x + y + z) + 16f(x) + 2f(y) − 2f(2x + y) −f(2x + z) − f(2x − z) − f(y + z) − f(y − z)k ≤ kf(2x + y − z)k and then investigate the generalized Hyers–Ulam stability of this inequality in Banach spaces and in non-Archimedean Banach spaces by using fixed point method and direct method, respectively.
2010 MSC. Primary 39B82;46S10.
On p-adic analogue of Weil’s elliptic functions according to Eisenstein
Min-Soo Kim Division of Cultural Education, Kyungnam University 7(Woryeong-dong) kyungnamdaehak-ro, Masanhappo-gu, Changwon-si Gyeongsangnam-do 631-701, Republic of Korea E-Mail: [email protected]
In this paper, using p-adic integration with values in spaces of modular forms, we construct the p-adic analogue of Weil’s elliptic functions according to Eisenstein in the book “Elliptic functions according to Eisenstein and and Kronecker”. This construction extends Serre’s p-adic family of Eisenstein series in “Formes modulaires et fonctions zˆeta p-adiques”. We show that the power series expansion of Weil’s elliptic functions also exists in the p-adic case. This is a joint work with Professor Su Hu. 2010 MSC. 11F33.
Some surjectivity results on maximal monotone operators 70
In-Sook Kim Department of Mathematics, Sungkyunkwan University Suwon 440-746, Republic of Korea E-Mail: [email protected]
Topological degree theory is an effective tool in the study of nonlinear equations in- cluding maximal monotone operators. In this talk, we are concerned with the solvability of a nonlinear inclusion about quasibounded maximal monotone operators in reflexive Banach spaces. To this end, we introduce a topological degree theory for densely defined perturbations of quasibounded maximal monotone operators, based on the Kartsatos- Skrypnik degree. The degree theory is used to prove an open mapping theorem from which a surjectivity result is deduced under a coerciveness condition. In a more con- crete situation, the existence of zeros for the inclusion is discussed, with a regularization method by means of the duality operator. 2010 MSC. Primary 47J05, 47H05; Secondary 47H11.
Eigenvalues of maximal monotone operators
In-Sook Kim and Jung-Hyun Bae∗ Department of Mathematics, Sungkyunkwan University Suwon 440-746, Republic of Korea Department of Mathematics, Sungkyunkwan University Suwon 440-746, Republic of Korea E-Mail: [email protected], [email protected]∗
In this talk, we deal with some eigenvalue results on maximal monotone operators in reflexive Banach spaces. The study is based on degree theories for appropriate classes of nonlinear operators and a regularization method by means of the duality operator. Let X be a real reflexive Banach space with its dual space X∗. Suppose that T : D(T ) ⊂ X → 2X∗ is a maximal monotone operator and C : D(C) ⊂ X → X∗ is a single-valued operator of (S+) type. We consider an eigenvalue problem of the form
0 ∈ T x + λCx. 71
The goal is to study the solvability of this problem in several classes of operators of (S+) type via the topological degree. When C is demicontinuous bounded and satisfies the condition (S+), it is investigated by applying the Browder degree for class (S+). For the case when C is densely defined and satisfies the condition (S+)D(C), we use a degree theory for (S+)L-perturbations of maximal monotone operators due to Kartsatos and Quarcoo. 2010 MSC. Primary 47H05, 47J10; Secondary 47H11.
Viscosity Approximation Method with Meir-Keeler Contractions for Common Zeros of Accretive Operators
Jong Kyu Kim Department of Mathematics Education, Kyungnam University Changwon 631-701, Republic of Korea E-Mail: [email protected]
The purpose of this talk is to introduce a new iterative process by the combination of the viscosity approximation with Meir-Keeler contractions and proximal point algorithm for finding common zeros of a finite family of accretive operators in a Banach space with a uniformly Gˆateauxdifferentiable norm. And we also give some applications of our results for the convex minimization problem and variational inequality problem in Hilbert spaces. The results of this paper improved and extend corresponding ones announced by many others 2010 MSC. 47H06, 47H09, 47H10, 47J25.
On weak Bloch functions
Ki Won Kim Department of Mathematics Education, Silla University 72
Busan 617-736, Republic of Korea E-Mail: [email protected]
We introduce a weak Bloch function which is a generalization of a Bloch function in terms of the quasihyperbolic metric and we give some charaterizations and properties of it. Then using the weak Bloch function, we charaterize a uniform domain and an inner uniform domain. In addition, using a Bloch function and a weak Bloch function, we give some properties of a φ-uniform domain which is a generalizaton of a uniform domain and of a φ-John domain which is a generalizaton of an inner uniform domain. 2010 MSC. Primary 30C65, 30F45; Secondary 30H30.
Estimates of the hyperbolic metric on the twice punctured plane
Seong-A Kim∗, Jinxi Ma and William Ma Department of Mathematics, Dongguk University, Gyeongju 780-714, Korea Department of Mathematics, Beihang University, Beijing 100083, P. R. China School of Sciences, Humanities & Visual Communications Pennsylvania College of Technology, PA 17701, U. S. A. ∗E-Mail: [email protected]
We provide various estimates on the hyperbolic metric of the twice punctured plane C\{0, 1} and apply them to improve Landau’s Theorem. We also improve Ahlfors’ upper bound on the hyperbolic metric of the twice punctured plane C\{0, 1}. 2010 MSC. Primary 30F45.
Ovarian cancer subtype classification using microRNA and their target mRNA 73
Shinuk Kim Department of Computer software engineering, Sangmyung University Cheonan, 330-720 Republic of Korea E-Mail: [email protected]
Ovarian cancer is the fifth leading cause of death from gynecological malignancy and 5year survival rate are only 5% 30% once in advanced stage. Identifying molecular biomarkers that aid long survival patients in cancer is a matter of great interest. Re- cently bio techniques allocate for high throughput data sets that of different molecular types (miRNA, Copy number, mRNA, and protein, etc.) from the same patient. Most previous works analyzed different level of data sets individually and then merge meaning- ful information. However, microRNAs (miRNAs) and their target mRNA is biologically negative in correlation, and sequence complementary binding target genes of miRNA provided from web sources contain numerous false positives. Regarding to this issue we presented a new method for integrative data sets especially miRNAs and their target mRNA. We used the relationship between microRNA and its target genes for generating new data sets which including both molecular expressions and biological information. Especially we tested the method using The Cancer Genome Analysis (TCGA) ovarian survival patients including long (greater than 5 years) and short (less than 1 year) sur- vival time. The presented methods also apply to identifying significant miRNA and its target gene simultaneously for aiding long survival patients. 2010 MSC. Primary 92B05, 92B99; Secondary 62P10, 90C90.
Further applications of the generalized Kumer summation theorem for the series 2F1
Yong Sup Kim and Arjun Kumar Rathie ∗ Department of Mathematics Education, Wonkwang University Iksan 570-749 Republic of Korea E-Mail: [email protected] Department of Mathematics, Central University of Kerala Kasaragod-671 328, India E-Mail: [email protected] 74
This paper is in continuation of the paper [Applications of generalized Kummer’s summation theorem for the series 2F1, Bull. Korean Math.Soc., 46(2009), No. 6, 1201 - 1211] in which we provide further applications of the generalized Kummer theorem obtained earlier by Lavoie et al.. The results derived in this paper are simple, interesting, easily established and may be useful in theoritical physics, engineering and mathematics. 2010 MSC. Primary 33C05, 42A16; Secondary 33C20.
A note on the almost sure and moment exponential stability for stochastic functional differential equations
Young-Ho Kim Department of Mathematics, Changwon National University Changwon 641-773, Republic of Korea E-Mail: [email protected]
The main objective of this talk is to present sufficient conditions ensuring the pth moment of and almost sure exponential stability of a stochastic functional differential equation of Itˆo-type. Under a monotone condition, we shall establish the asymptotic estimate for the solution of stochastic functional differential equations. 2010 MSC. Primary 60H10, 60H30.
Asymptotic behavior of the quaternion linear canonical Transform and the Bochner-Minlos Theorem
Kit Ian Kou and Joao Morais Department of Mathematics, Faculty of Science and Technology, University of Macau Avenida da Universidade, Taipa, Macau, China E-Mail: [email protected] 75
There have been numerous proposals in the literature to generalize the classical Fourier transform by making use of the Hamiltonian quaternion algebra. The present talk re- views the quaternion linear canonical transform (QLCT) which is a generalization of the quaternion Fourier transform and it studies a number of its properties. In the first part of this paper, we establish a generalized Riemann-Lebesgue lemma for the (right-sided) QLCT. This lemma prescribes the asymptotic behaviour of the QLCT extending and re- fining the classical Riemann-Lebesgue lemma for the Fourier transform of 2D quaternion signals. We then introduce the QLCT of a probability measure, and we study some of its basic properties such as linearity, reconstruction formula, continuity, boundedness, and positivity. Finally, we extend the classical Bochner-Minlos theorem to the quaternion linear canonical transform setting showing the applicability of our approach. 2010 MSC. Primary 30G35; Secondary 42A38, 42A82.
On best proximity point theorems in metric spaces
Poom Kumam Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) 126 Pracha Uthit Rd., Bang Mod, Thrung Khru, Bangkok 10140, Thailand E-Mail: [email protected]
There has been some cases in the literature where the problem T x = x has no solution. In this situation, we may consider another general problem, the best proximity point problem, which is our main concern in this talk. Roughly speaking, we discuss the existence of best proximity points for nonlinear operators in metric spaces.
Some Identities and Recurrence Relations on the Two variables Bernoulli, Euler and Genocchi Polynomials
Veli Kurt and Burak Kurt 76
Department of Mathematics, Akdeniz University Antalya, Turkey E-Mail: [email protected]; [email protected]
In this article, we give some identities for the q-Bernoulli polynomials, q-Euler poly- nomials and q-Genocchi polynomials and recurrence relation between these polynomials. We give different form of the analogue of the Srivastava-Pint´eraddition theorem. 2010 MSC. Primary 05A10, 11B65; Secondary 11B68, 28B68.
References [1] Carlitz L.: Expansions of q-Bernoulli numbers, Duke Math. J., 25 (1958), 355-364. [2] Luo Q.-M.: Some results for the q-Bernoulli and q-Euler polynomials, J. Math. Analy. Appl. 363 (2010), 7-18. [3] Kim D., Kurt B. and Kurt V.: Some identities on the generalized q-Bernoulli, q-Euler and q-Genocchi polynomials, Abstract and Appl. Analy., vol 2013, article ID 293.352, doi:10.1155/2013/293532. [4] Kurt V.: New identities and relations derived form the generalized Bernoulli polynomials, Euler polynomials and Genocchi polynomials, Adv. in Difference Equ. 2014, doi:10.1186/1687-1847-2014-5. [5] Mahmudov N. I.: q-analogues of the Bernoulli and Genocchi polynomials and the Srivastava-Pint´er addition theorems, Discrete Dyn. Nat. Soc. 2012, Article ID 169348 (2012), doi: 10.1155/2012/169348. [6] Mahmudov N. I.: On a class of q-Bernoulli and q-Euler polynomials, Adv. in Difference equ. 2013. [7] Srivastava H. M. and Choi J.: Series associated with the zeta and related functions, Kluwer Academic, London, 2001.
n Mean Lipschitz spaces on the unit ball of C
E. G. Kwon Department of Mathematics, Andong National University Andong 760-749, Republic of Korea E-Mail: [email protected]
n On the unit ball of C , the space of those holomorphic functions satisfying mean Lipschitz condition Z 1 Z 1 q dt ∗ q dt ωp(t, f) 1+αq < ∞ resp. ωp(t, f) 1+αq < ∞ 0 t 0 t 77
is characterized by integral growth conditions of the tangential derivatives as well as the ∗ p radial derivatives, where ωp(t, f) resp. ωp(t, f) denotes the L modulus of continuity (resp. the double difference Lp modulus of continuity) defined in terms of the unitary n transformations of C . 2010 MSC. Primary 32A30, 30H25.
On the argument properties of analytic functions with fixed second coefficients
Ohsang Kwon Department of Mathematics, Kyungsung University Busan 608-736, Korea E-Mail: [email protected]
In this paper, we investigate some argument properties for analytic functions with fixed second coefficient and positive real part. And, we apply the argument properties to the functions that are analytic and normalized. In particular, the order of strongly starlikeness of strongly convex functions with fixed second coefficients is given. 2010 MSC. Primary 30C45; Secondary 30C55.
Ekeland’s variational principle and fixed point theorems in quasi-partial metric spaces
Chirasak Mongkolkeha∗ Department of Mathematics, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng-Saen Campus, Nakhonpathom 73140, Thailand E-Mail: [email protected] Tamaki Tanaka 78
Graduate School of Science and Technology, Niigata University, Niigata-City 950-2181, Japan Poom Kumam Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) Bangmod, Thrungkru, Bangkok 10140. Thailand
In this talk, we prove some general Ekeland variational principle in quasi-partial metric spaces and also prove fixed point theorems in this spaces. Moreover, we give some example for support our result.
On stability results for perturbed polynomial optimization problems
Gue Myung Lee∗ Department of Applied Mathematics, Pukyong National University, Busan 608-737, Korea E-Mail: [email protected] Tien Son Pham Department of Mathematics, University of Dalat, 1, Phu Dong Thien Vuong, Dalat, Vietnam E-Mail: [email protected]
We consider polynomial optimization problem, the problem of minimizing (maximiz- ing) a polynomial function over the constraint set defined by polynomial functions. Sta- bility results for perturbed polynomial optimization problems are presented. Main tools for our investigation come from semi-algebraic geometry. We establish the upper semi- continuity, the lower semicontinuity and the set-valued differentiability of Karush-Kuhn- Tucker set-valued maps and global solution maps for polynomial optimization problems with perturbed objective functions. Moreover, we give explicit formulas for computing the directional derivative and the subgradient, the (Fr´echet) derivative of the optimal value function. 2010 MSC. Primary 90C26; Secondary 90C31 79
Unitary orbits and decompositions of positive matrices
Eun-Young Lee Department of Mathematics, Kyungpook National University Daegu, Republic of Korea E-Mail: [email protected]
A number of elegant matrix/operator is obtained with a unitary orbit technique. Subadditivity type inequalities are considered. Various trace, norm and determinantal inequalities are derived. Combined with an interesting decomposition for positive semi- definite matrices, several results for partitioned matrices are also obtained. 2010 MSC. Primary 15A60, 47A30 ; Secondary 47A60, 15A42.
Half lightlike submanifolds of a semi-Riemannian manifold of quasi-constant curvature
Jaewon Lee School of General Education, Yeungnam University Gyeongsan 712-749, Republic of Korea E-Mail: [email protected]
In the generalization from the theory of submanifolds in Riemannian manifolds to the theory of submanifolds in semi-Riemannian manifolds, the induced metric on subman- ifolds may be degenerate( lightlike). Therefore, there is a natural existence of lightlike submanifolds, whose the local and global geometry is completely different than non- degenerate case. In lightlike case, the standard text book definitions do not make sense and one fails to use the theory of non-degenerate geometry in the usual way. We study the geometry of half lightlike submanifolds (M, g, S(TM),S(TM ⊥)) of a semi-Riemannian manifold (M,f ge) of quasi-constant curvature subject to the following conditions; (1) the curvature vector field ζ of Mf is tangent to M, (2) the screen distribution S(TM) of M is either totally geodesic or totally umbilical in M, and (3) the coscreen distribution S(TM ⊥) of M is a conformal Killing distribution. ( joint work with Daeho Jin) 80
2010 MSC: 53C25, 53C40, 53C50.
New criteria for Carath´eodory functions
Hyo Jeong Lee∗ and Nak Eun Cho Department of Applied Mathematics, Pukyong National University Busan 608-737, Republic of Korea E-Mail: [email protected]; [email protected]
The purpose of the present talk is to introduce some sufficient conditions for Carath´eodory functions by using the results given by Miller and Mocanu, and Nunokawa. Applications of our main results to geometric function theory are also given. 2010 MSC. Primary 30C45; Secondary 30C80.
A fixed point approach to the stability of an AQCQ-functional equation in RN-spaces
Jung Rye Lee1, Choonkil Park2, Cihangir Alaca3 and Dong Yun Shin4 1Department of Mathematics, Daejin University Kyeonggi 487-711, Republic of Korea E-Mail: [email protected] 2Department of Mathematics, Hanyang University Seoul 133-791, Republic of Korea 3Department of Mathematics, Celal Bayar University 45140 Manisa, Turkey 4Department of Mathematics, University of Seoul Seoul 130-743, Republic of Korea 81
E-Mail: [email protected]; [email protected]; [email protected]
Using the fixed point method, we prove the Hyers-Ulam stability of the following additive-quadratic-cubic-qurtic functional equation
f(x+2y)+f(x−2y) = 4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)
in random normed spaces. 2010 MSC. Primary 39B52, 54E70, 47H10, 54E40.
A Coburn type theorem for Toeplitz operators on the Dirichlet space
Young Joo Lee Department of Mathematics, Chonnam National University Gwangju 500-757, Korea E-mail:[email protected]
A celebrated theorem of Coburn asserts that, on the setting of the Hardy space, if a Toeplitz operator is nonzero, then either it is one-to-one or its adjoint operator is one- to-one. In this talk, we show that an analogous result holds for Toeplitz operators acting on the Dirichlet space. 2010 MSC. Primary 47B35; Secondary 32A36.
The complex differential and difference equations 82
and their applications
Liangwen Liao Department of Mathematics, Nanjing University Nanjing, China E-Mail: [email protected]
In this talk, we will present some new results about solving nonlinear differential equations by using Wiman-Valiron theory and Nevanlinna theory in the value distri- butions of meromorphic functions, especially, Clunie lemma. We also prove the some extend Hayman’s theorems about differential polynomials. We discuss algebraic differ- ential equations with admissible meromorphic solutions. Furthermore, we discuss the uniqueness of the entire functions which share some value with their difference operators or derivatives. 2010 MSC. Primary 30D35; Secondary 34D05, 30D30.
The history and study for Ramanujan’s circular summation
Qiu-Ming Luo Department of Mathematics, Chongqing Normal University Chongqing 401331, People’s Republic of China E-Mail: [email protected]
On page 54 in the Ramanujan’s lost notebook, Ramanujan recorded the following claim (without proof) which is now well known as Ramanujan’s circular summation. For each positive integer n and |ab| < 1, n ∞ X X k(k+1)/(2n) k(k−1)/(2n) a b = f(a, b)Fn(ab), −n/2 ∞ X f(a, b) = an(n+1)/2bn(n−1)/2, |ab| < 1. n=−∞ The function f(a, b) is called Ramanujan’s theta function. We here introduce the history and study for Ramanujan’s circular summation formula. The appellation circular summation was initiated by Seung Hwan Son. 2010 MSC. Primary 11F27; Secondary 11F20, 33E05. Bilipschicity of Quasiconformal Harmonic Mappings Vesna Manojlovi´c Mathematical Institute SASA, FOS University of Belgrade Belgrade, Republic of Serbia E-Mail: [email protected] 2 We show that quasiconformal harmonic mappings on the proper domains in R are bilipschitz with the respect to the quasihyperbolic metric. Possible generailzation in higher dimensions are given. 2010 MSC. Primary 30C65; Secondary 30C62. Holomorphic mappings of once-holed tori into Riemann surfaces of positive genus Makoto Masumoto Department of Mathematics, Yamaguchi University Yamaguchi 753-8512, Japan E-Mail: [email protected] 84 A once-holed torus is a noncompact Riemann surface of genus one with exactly one boundary component. It is thus homeomorphic to a torus with one point deleted; note that once-holed tori are not bordered surfaces. We address the existence problem of handle-preserving holomorphic mappings of once-holed tori into a given Riemann surface of positive genus. The general uniformization theorem asserts that every Riemann surface of genus zero is conformally equivalent to a plane domain. Thus function theory on such Riemann surfaces is, in a sense, part of function theory on plane domains. Therefore the core of theory of Riemann surfaces should be occupied by Riemann surfaces of positive genus, that is, those with handles. Once-holed tori are the simplest among the Riemann surfaces of positive genus. A Riemann surface is of positive genus if and only if it includes a once- holed torus as a subdomain. Moreover, every Riemann surface of positive genus g is made of g once-holed tori. In other words once-holed tori are building blocks of Riemann surfaces of positive genus. Hence function theory on once-holed tori is of fundamental importance. Once-holed tori should play a similar role to that played by open disks in function theory on plane domains. However, while open disks are conformally equivalent to one another, once-holed tori are not. The Teichm¨ullerspace T of a once-holed torus is a 3-dimensional real analytic manifold with boundary. For a given Riemann surface Y0 of positive genus with marked handle we investigate the set Ta[Y0] of X ∈ T such that there is a holomorphic mapping of X into Y0 whose image corresponds to the marked handle of Y0. We also examine some subsets of Ta[Y0] concerning the existence of holomorphic mappings. It turns out that these sets, including Ta[Y0], have some geometric properties of special character in common. 2010 MSC. Primary 30F99. A certain circle diffeomorphism with H¨oldercontinuous derivative Katsuhiko Matsuzaki Department of Mathematics, School of Education, Waseda University Shinjuku, Tokyo 169-8050, Japan E-Mail: [email protected] We give the following example of an orientation preserving deffeomorphism of the unit circle g : S → S having an α-H¨oldercontinuous derivative for α ∈ (0, 1): there is −1 an orientation preserving diffeomorphism f : S → S such that the conjugate f gf is a 85 M¨obiustransformation of S but there is no such f with α-H¨oldercontinuous derivative. Note that if the conjugate f −1gf is a hyperbolic transformation, then the conjugating map f always has an α-H¨oldercontinuous derivative. 2010 MSC. Primary 37E10; Secondary 30F60. Generalized quadrature formulae and multiple orthogonal polynomials Gradimir V. Milovanovi´c Mathematical Institute of the Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia E-Mail:[email protected] In this paper we give a new application of the so-called multiple orthogonal polyno- mial, which are also known as Hermite-Pad´epolynomials (cf. Aptekarev [J. Comput. Appl. Math. 99 (1998), pp. 423–447]). Namely, we consider a class of generalized quadrature formulae of Birkhoff–Young type for analytic functions in the complex plane and give a direct connection with multiple orthogonal polynomials. Precisely, we give a characterization of such generalized quadratures in terms of multiple orthogonal poly- nomials and prove the existence and uniqueness of these quadratures. Some interesting properties of the multiple orthogonal polynomials were investigated in the last twenty years. An application to Borges quadratures [Numer. Math. 67 (1994), 271–288] was given by Milovanovi´cand Stani´c[Facta Univ. Ser. Math. Inform. 18 (2003), 9–29]. 2010 MSC. Primary 65D30, 65D32; Secondary 33C45, 42C05. This work was supported in part by the Serbian Ministry of Education, Science and Technological Development. Sobolev’s inequality in Herz-Morrey spaces of variable exponent and duality 86 Yoshihiro Mizuta Department of Mechanical Systems Engineering Hiroshima Institute of Technology 2-1-1 Miyake Saeki-ku Hiroshima 731-5193, Japan E-Mail: [email protected] Let p(·) be a variable exponent on a bounded open set G whose diameter is denoted by dG, and take x0 ∈ G. Our first aim in this talk is to discuss the boundedness of the maximal and potential operators in Herz-Morrey spaces Hp(·),q,ν(G) of all measurable {x0} functions f on G satisfying 1/q Z dG q −ν kfk p(·),q,ν = r kfk p(·) dr/r < ∞ H (G) L (B(x0,r)) {x0} 0 for −∞ < ν < ∞ and 0 < q ≤ ∞; when q = ∞, we apply a necessary modification. Note here that \ p(·),∞,ν Hp(·),∞,ν(G) = H (G) {x0} x0∈G is the usual Morrey space. p(·),q,ν In connection with Hp(·),q,ν(G), we treat the space H (G) of all measurable func- {x0} {x0} tions f satisfying 1/q Z dG q −ν kfk p(·),q,ν = r kfk p(·) dr/r < ∞. H (G) L (G\B(x0,r)) {x0} 0 p0(·),q0,−ν The duality between Hp(·),q,ν(G) and H (G) is also discussed. {x0} {x0} 2010 MSC. Primary 31B15; Secondary 46E35. Common fixed point theorems under generalized W-weakly contractive condition Hemant Kumar Nashine Department of Mathematics, Disha Institute of Management and Technology Satya Vihar, Vidhansabha-Chandrakhuri Marg, Mandir Hasaud, Raipur-492101(Chhattisgarh), India. 87 E-Mail: [email protected] We propose coincidence and common fixed point results for two pairs (A, T ) and (B,S) of partially weakly increasing mappings where A and B are dominating maps; B is weak annihilator of S and T is weak annihilator of A in a ordered complete metric space (X, d) under a generalize W-weakly contractive condition: ( 1 ) d(Ax, Sx), d(By, T y), d(T y, Sx), 2 [d(Ax, T y) + d(By, Sx)], d(Ax, By) ≤ max d(Ax,Sx)d(By,T y) d(Ax,T y)d(By,Sx) d(Ax,T y)d(By,Sx) 1+d(T y,Sx) , 1+d(T y,Sx) , 1+d(Ax,By) ( 1 )! d(Ax, Sx), d(By, T y), d(T y, Sx), 2 [d(Ax, T y) + d(By, Sx)], −W max d(Ax,Sx)d(By,T y) d(Ax,T y)d(By,Sx) d(Ax,T y)d(By,Sx) 1+d(T y,Sx) , 1+d(T y,Sx) , 1+d(Ax,By) for all x, y ∈ X and W ∈ Ψ, where Ψ the collection of all the functions W : [0, ∞) → [0, ∞) which are continuous and satisfy W(t) < t, for all t > 0. 2010 MSC. Primary 47H10; Secondary 54H25. Common fixed point results for gα-approximative multivalued mappings in metric spaces Aphinat Ninsri and Wutiphol Sintunavarat Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand E-Mail: [email protected]; [email protected] In this talk, we introduce the concepts of weakly Lα-idempotent and weakly Rα- idempotent mappings and give some example for these mappings. Also, we define the gα- approximative multivalued mappings. Further, we establish common fixed point results for gα-approximative multivalued mappings in metric spaces. 2010 MSC. 47H09; 47H10. 88 Holomorphic extensions of invariant holomorphic functions with a complex Lie group action Masaru Nishihara Department of Computer Science and Engineerings Fukuoka Institute of Technology Fukuoka 811-0295, Japan E-Mail: mr-nisi@fit.ac.jp Let E be a complex Banach space and let (Ω, ϕ) be a Riemann domain over E. Let G be a complex Lie group. We denote by e the unit element of G. A holomorphic mapping (g, x) ∈ G × Ω → g · x ∈ Ω satisfying the following properties is called a holomorphic G-action on Ω: (1) e · x = x for every x ∈ Ω. (2) (g1 · g2)x = g1 · (g2 · x) for any x ∈ Ω and any g1, g2 ∈ G. A subdomain ω of Ω is said to be G-invariant domain if g · x ∈ ω for every (g, x) ∈ G × Ω. A holomorphic function f in G-invariant domain ω is said to be G-invariant if f(g · x) = f(x) for every (g, x) ∈ G × ω. In this talk we discuss holomorphic extensions of G-invariant holomorphic functions in G-invariant domain ω. 2010 MSC. Primary 46G20, 58B12; Secondary, 32D10, 32D15 Two dimensional Chlodowsky variant of q-Bernstein-Schurer-Stancu operators Mehmet Ali O¨ zarslan and Tuba Vedi Department of Mathematics, Eastern Mediterranean University Gazimagusa, TRNC, Mersin 10 , Turkey E-Mail: [email protected] and [email protected] 89 In this paper, two-dimensional Chlodowsky variant of q-based Bernstein-Schurer- Stancu operators are introduced. Korovkin-type approximation theorems in different function spaces are studied. The error of approximation by using modulus of continuity and Lipschitz-type functionals are given. Moreover, we study the generalization of the two-dimensional Chlodowsky variant of q-Bernstein-Schurer-Stancu operators and seek their approximations. 2010 AMS Math. Subject Classification. Primary 41A10, 41A25; Secondary 41A36. On multiplication formula of the modification and unification of Apostol-type polynomials Hacer Ozden and Yilmaz Simsek University of Uludag, Faculty of Arts and Science, Department of Mathematics Bursa, Turkey Akdeniz University Faculty of Science Department of Mathematics 07058 Antalya, Turkey E-Mail: [email protected]; [email protected] The aim of this paper is to give multiplication formula for the modification and unifi- cation of Apostol-type polynomials. We derive some remarks and observation from this formula. By using functional equations and PDEs of the generating functions for these polynomials, we derive some identities and relations of these polynomials. 2010 MSC. 11B68, 11S40, 11S80, 11M99, 30B50, 44A05. Quadratic ρ-functional inequalities and equations Choonkil Park Department of Mathematics, Hanyang University 90 Seoul 133-791, Republic of Korea E-Mail: [email protected] We investigate the quadratic ρ-functional inequalities kf(x + y) + f(x − y) − 2f(x) − 2f(y)k (1) x + y x − y ≤ ρ 2f + 2f − f(x) − f(y) , 2 2 where ρ is a fixed complex number with |ρ| < 1, and x + y x − y 2f + 2f − f(x) − f(y) (2) 2 2 ≤ kρ(f(x + y) + f(x − y) − 2f(x) − 2f(y))k, 1 where ρ is a fixed complex number with |ρ| < 2 . Furthermore, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequali- ties (1) and (2) in complex Banach spaces and prove the Hyers-Ulam stability of quadratic ρ-functional equations associated with the quadratic ρ-functional inequalities (1) and (2) in complex Banach spaces. 2010 MSC. Primary 39B62, 39B72, 39B52. Notes on multivalently meromorphic starlikeness Ji Hyang Park∗ and Nak Eun Cho Department of Applied Mathematics, Pukyong National University Busan 608-737, Republic of Korea E-Mail: [email protected]; [email protected] The purpose of the present paper is to obtain some sufficient conditions for multiva- lently meromorphic starlikeness in the punctured open unit disk. 2010 MSC. 30C45. 91 Fuzzy stability of radical quartic functional equation via fixed point approach Supak Phiangsungnoen and Poom Kumam Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) 126 Pracha Uthit Rd., Bang Mod, Thrung Khru, Bangkok 10140, Thailand E-Mail: supuk [email protected]; [email protected] We establish the generalized Hyers-Ulam stability of radical quartic functional equa- tion in fuzzy Banach spaces via fixed point method. 2000 MSC. Primary 39B72, 39B82, 39B52, 47H09 Resolution of nontrivial diophantine equations without reduction methods Akos´ Pint´er Institute of Mathematics, University of Debrecen H-4032, Egyetem t´er1, Debrecen, Hungary E-Mail: [email protected] We present a new method to resolve certain diophantine equations including a gener- alization of a classical problem by Mordell. The crucial point of our approach is the gap between two consecutive solutions of a Pellian equation. The talk is based on some joint works with Alain Togb´eand N´oraVarga. 2010 MSC. Primary 11D25. Alternating Mathieu series and their generalized Omega functions 92 Tibor K. Pog´any Faculty of Maritime Studies, University of Rijeka 51000 Rijeka, Republic of Croatia E-Mail: [email protected] In this talk our aim is to generalize the complete Butzer–Flocke–Hauss (BFH) Ω- function in a natural way by introducing the generalized Omega–function via alternating generalized Mathieu series by imposing Bessel function of the first kind of arbitrary order as the kernel function instead of the original cosine function in the integral definition of the Ω. We also study the following set of questions concerning generalized BFH Ων- function: (i) two different sets of bounding inequalities by certain bounds upon the kernel Bessel function; (ii) linear ordinary differential equation of which a particular solution is the newly introduced Ων-function, and another set of bounding inequalities are given by virtue of the Caplyginˇ comparison theorem. 2010 MSC. Primary 26D15, 33E20, 34A30, 39B62; Secondary 33C10, 33E30, 39B72. Quadratic forms involving Neumann function Elena Prilepkina Far Eastern Federal University and IAM FEBRAS Vladivostok, Russia E-Mail: [email protected] General inequalities for quadratic forms with coefficients depending on the values of Green’s and Robin functions have many applications in geometric theory of functions. These forms were further studied by Nehary, Alenitsyn, Duren, Schiffer and other math- ematicians. Dubinin in [1] established the connection of such forms with a capacity of degenerate condenser. In this report we will discuss the properties of quadratic forms with coefficients depending on the values of Neumann function. According to Dubinin approach we obtained an asymptotic formula for the capacity of corresponding degener- ate condenser in [2]. We denote by nB(z; ζ) the Neumann function of domain B with pole at the point ζ. For example, the next result follows from the monotonicity of the capacity. Suppose B, 93 D are finitely-connected domains without isolated boundary points, f(z) is conformal n P univalent mapping of B, f(B) ⊂ D, and real numbers δk satisfy the condition δk = 0. k=1 Then n n n X X X 2 0 δkδlNkl(B) ≥ δkδlNkl(D) − δk log |f (zk)|. k,l=1 k,l=1 k=1 Here Nkl(B) := nB(zk; zl),Nkl(D) := nD(f(zk); f(zl)), k 6= l, Nkl(B) := lim (nB(z; zk) + log |z − zk|), z→zk Nkl(D) := lim (nD(w; f(zk)) + log |w − f(zk)|), k = l. w→f(zk) As a consequence we proved new distortion theorems for univalent functions defined in the unit disk and in the annulus. In addition, estimates for Schwarz derivative were derived. We also consider the transfinite diameter with respect to Neumann function. This diameter coincides with Robin capacity. We obtained the representations of this size in terms of the condenser capacity and Dirichlet integral of some function. [1] V.N. Dubinin. Generalized condensers and the asymptotics of their capacities under degeneration of some plates. J. Math. Sci., 129:3, (2005), 3835-3842. [2] Karp D., Prilepkina E. Reduced modules with free boundary and its applications // Annales Academi Scient. Fen., V.34,(2009), 353-378. 2010 MSC: Primary 30C10; Secondary 30C85 Integral representations and properties of some functions involving the logarithmic function Feng Qi and Wen-Hui Li Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin City, 300387, China E-Mail: [email protected], [email protected], [email protected] URL: http://qifeng618.wordpress.com By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such as being operator 94 monotone function, being complete Bernstein function, and being Stieltjes function, for these functions, and verify a conjecture on complete monotonicity of a function involving the logarithmic function. 2010 MSC. Primary 30E20; Secondary 26A12, 26A48, 33B99, 44A20. Use of quaternions in molecular biology J. R. Quine Department of Mathematics, Florida State University Tallahassee, FL USA E-Mail:[email protected] Quaternions are often used to compute compositions of rotations in 3-D space. A convenient formula is an analogue of Euler’s formula: if P is a pure unit quaternion then the quaternion eP θ/2 describes rotation an angle θ around the axis given by the vector P . In the study of long molecules such as proteins, a string of atoms is modeled as a discrete curve with a sequence of Frenet frames along the curve. The curve can be computed from a sequence of torsion angles which describe rotations between adjacent frames. Regular repeating torsion angles give helices, and the axis of the helix can be computed by multiplying a sequence of quaternions. Proteins form helical structures and this method can be useful in computing the 3D structure of a protein from experimental data giving orientations of the Frenet frames with respect to a fixed lab frame. This type of data can be obtained from nuclear magnetic resonance (NMR), and important membrane proteins have been “seen” by this method. 2010 MSC. Primary 92E10; Secondary 53A04 Non-local boundary value problem for mixed parabolic-hyperbolic type equation 95 Nilufar Rakhmatullaeva Department of Higher Mathematics, Tashkent State Technical University Beruniy str.2, Tashkent, Uzbekistan E-Mail: [email protected] In the present talk we investigate a boundary value problem with non-local condi- tions for mixed parabolic-hyperbolic type equation with three lines of type changing. Considered domain contains a rectangle as a parabolic part and three domains bounded by smooth curves and type-changing lines as a hyperbolic part of the mixed domain. Applying method of energy integrals we prove the uniqueness of the solution for the considered problem. The proof of the existence will be done by reducing the original problem into the system of the second kind Volterra integral equations. 2010 MSC. Primary 35M12; Secondary 45D05. Generalizations of Preece’s and Bailey’s hypergeometric identities involving products of generalized hypergeometric series with applications Arjun K. Rathie Department of Mathematics, Central University of Kerala Kasaragod-671123, Kerala State, INDIA E-Mail: [email protected] The aim of this contributed talk is to discuss about the unified result 1F1 (α; 2α ± i; x) 1F1 (β; 2β ± j; x) in the most general case for any i, j = 0, 1, 2,... . For i = j = 0, we get the well known Bailey’s identity (which is the generalization of the Preece’s identity) involving product of generalized hypergeometric series. As special cases, explicit expressions for the square of generalized hypergeometric series viz. 2 {1F1 (α; 2α ± i; x)} for any i = 0, 1, 2,... have also been given. In the last, a few applications of the results will also be discussed. 96 2010 MSC. Primary 33C05; 33C65; Secondary 33C60; 33C70 On a problem with two non-local boundary conditions for the degenerated elliptic type equation with singular coefficient and spectral parameter M. Kh. Ruziev Institute of Mathematics National University of Uzbekistan Durman yuli 29, 100125,Tashkent, Uzbekistan E-Mail: [email protected] Consider the equation β ymu + u + 0 u − λ2ymu = 0, (1) xx yy y y in the vertical half-band D = {(x, y) : 0 < x < 1, y > 0}. Let D = D ∪ J0 ∪ OB ∪ J1, where J0 = {(x, y): x = 0, y > 0}, J1 = {(x, y): x = 1, y > 0}, O(0, 0),B(1, 0),m > 0,−m/2 < β0 < 1,λ ∈ R. Problem F . To find a function u(x, y) with properties: 1 2 1) u(x, y) ∈ C(D) ∩ C (D ∪ J0 ∪ J1) ∩ C (D) and satisfies the equation (1) in D; 2) lim u(x, y) = 0 is uniform by x ∈ [0, 1]; y→+∞ 3) u(0, y) − u(1, y) = ϕ1(y), y > 0; ux(0, y) − ux(1, y) = ϕ2(y), y > 0; β 4) lim y 0 uy = ν(x), x ∈ [0, 1]. y→+0 Here ϕ1(y),ϕ2(y) and ν(x) are given functions. The uniqueness of solution of the problem is proved by an extremum principle. Theorem. Let the following conditions be fulfilled: 1 ϕi(y) ∈ C[0, ∞) ∩ C (0, ∞), lim ϕi(y) = 0, y→+∞ 3m+2β0 2 y 4 ϕi(y) ∈ L(0, ∞), i = 1, 2, ν(x) ∈ C [0, 1] and on the segment [0, 1] has third order piecewise-continuous derivatives, ν(0) = ν(1), ν00(0) = ν00(1). Then the solution of the problem F exists. By the variable separation method, using Hankel transformation , we prove the unique solvability of the problem F . 2000 MSC. Primary 35J25,35M99; 97 On fixed point algorithm for solving the constrained convex optimization problem Plern Saipara and Poom Kumam Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) 126 Pracha Uthit Rd., Bang Mod, Thrung Khru, Bangkok 10140, Thailand E-Mail: [email protected]; [email protected] In this paper, we introduce the iterative process for finding a common element of the set of fixed points, equilibrium and variational inequality problems for strictly nonexpan- sive mappings. We provide algorithm which strong convergence theorems are obtained in Hilbert spaces. Then, we apply these algorithm to solve some convex optimization problems. The results of this paper extend and improve several results presented in the literature in the recent past. 2000 MSC. Primary 39B72, 39B82, 39B52, 47H09 Bases transforms in SO(3, 1)- and SO(2, 2)-representation spaces and formulas for related special functions I. A. Shilin Department of Mathematics, Sholokhov Moscow State University for the Humanities Verhnya Radishevskaya 16 - 18, Moscow 109240, Russia E-Mail: [email protected] Junesang Choi Department of Mathematics, Dongguk University Gyeongju 780-714, Republic of Korea E-Mail: [email protected] By using some bilinear functionals defined on a direct product of representation spaces and satisfying certain properties of invariance with respect to the corresponding indefinite 98 special orthogonal group, we compute the matrix elements of bases transforms operators acting in the representation space of group SO(3, 1) or SO(2, 2). These results, obtained for the spherical, hyperbolic, and parabolic bases, follows us to new formulas for special functions either included into bases vectors, or arising in matrix elements. 2010 MSC. Primary 33C10, 33C80; Secondary 33B15, 33C05. A fixed point approach to the fuzzy stability of an AQCQ-functional equation Dong Yun Shin1, Choonkil Park2, Reza Saadati3 and Themistocles M. Rassias4 1Department of Mathematics, University of Seoul Seoul 130-743, Republic of Korea E-Mail: [email protected] 2Department of Mathematics, Hanyang University Seoul 133-791, Republic of Korea 3Department of Mathematics, Iran University of Science and Technology Tehran, Iran 4Department of Mathematics, National Technical University of Athens Zografou Campus, 15780 Athens, Greece E-Mail: [email protected]; [email protected]; [email protected] The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using the fixed point method, we prove the Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x + 2y) + f(x − 2y) = 4f(x + y) + 4f(x − y) − 6f(x) + f(2y) + f(−2y) − 4f(y) − 4f(−y) in fuzzy Banach spaces. 2010 MSC. Primary 47H10, 39B52, 54E40, 46S40, 26E50. 99 The regularity of functions on dual split quaternions Kwang Ho Shon Department of Mathematics, Pusan National University Busan 609-735, Republic of Korea E-Mail: [email protected] A dual quaternion can be represented in the form which is ordinary quaternions and is the dual symbol. Since a dual quaternion algebra is constructed from real eight- dimensional vector spaces and an ordered pair of quaternions, the dual quaternion is used in applications to computer vision. We show that some properties of dual split quaternion numbers and expressions of power series in dual split quaternions. We give some properties of differential operators in dual split quaternions and a dual split regular function on the domain that has a dual split corresponding Cauchy-Riemann system in dual split quaternions. 2010 MSC. Primary 30G35, 11E88; Secondary 32A99, 32W50. A certain subclass of meromorphic functions Young Jae Sim Department of Mathematics, Kyungsung University Busan 608-736, Republic of Korea E-Mail: [email protected] Oh Sang Kwon Department of Mathematics, Kyungsung University Busan 608-736, Republic of Korea E-Mail: [email protected] For real α and β such that 0 ≤ α < 1 < β, we denote by Σ(α, β) the class of 0 normalized analytic functions such that α < Re(zf (z)/f(z)) < β in D. We investigate 100 some coefficient estimates for functions in the above class. Also, we investigate some properties for functions related to the bi-univalent functions. 2010 MSC. Primary 30C45; Secondary 30C55. Remarks on combinatorial identities related to special polynomials Yilmaz Simsek Akdeniz University Faculty of Science Department of Mathematics 07058 Antalya, Turkey E-Mail: [email protected] The aim of this paper is to derive some combinatorial identities which are associated with binomial coefficients, combinatorial sums and the Catalan numbers. By using identities on the Bernstein basis functions and beta-type polynomials, we investigate other combinatorial identities. 2010 MSC. 08A40, 11B83, 26C05, 26C15, 44A10. A new approach to (α, ψ)-contractive mappings and generalized Ulam-Hyers stability, well-posedness and limit shadowing Wutiphol Sintunavarat Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand. E-Mail: [email protected] 101 In this talk, we introduce the new concept of weakly α-admissible mapping and give example to show that our new concept is different from the concept corresponding ex- isting in the literature. We also establish fixed point theorems by using this new notion along with (α, ψ)-contractive condition. Moreover, we study the generalized Ulam-Hyers stability, the well-posedness and the limit shadowing of the fixed point problem for fixed point problems satisfy our conditions. 2010 MSC. Primary 47H10; Secondary 54H25. Multi-monogenic functions taking value in Clifford algebra depending on parameters Le Hung Son School of Applied Mathematics and Informatics Hanoi University of Science and Technology 2 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam E-Mail: [email protected] Clifford algebra depending on parameters is introduced by W.Tutschke, C.J.Vanegas in [1]. The main goal of this paper is to study some problems of function theory tak- ing value in such Clifford algebras.Firstly the generalized Cauchy Riemann operators is introduced. Based on those new concepts more general systems of partial differential equations as this is possible in framework of classical Clifford analysis are described. Furthermore a class of mutti monogenic functions taking value in a Clifford algebra de- pending on parameters more carefully studied, then some interesting relations between this class with the family of holomorphic functions on several complex variables. Finally using the theory of Clifford algebra depending on parameters (see [2, 3]) the concept of separately monogenic functions is introduced and the main problems of function theory on separately monogenic functions are studied. 2010 MSC. 30G35, 35F30, 35F105 References [1] E. Escassut, W. Tutschke and C. C.Yang (eds.), Some topics on value distribution and differentia- bility in complex and p-adic analysis, Science Press Beijing (2009).pp.430-449 [2] Le Hung Son and Tutschke (eds.), Algebraic Structures in Partial Differential Equations related to Complex and Clifford Analysis, Ho Chi Minh City University of Education Press ,2011, pp. 67–78. 102 [3] Le Hung Son, W.Tutschke and Sapna Jain (eds.), Methods of Complex and Clifford Analysis, SAS International Publications, Dehli,2004, pp. 113–122. Identities of symmetry for the higher order q-Bernoulli polynomials Jin-Woo Son Department of Mechanical Engineering, Kyungnam University Changwon 631-701, Republic of Korea E-Mail: [email protected] The study of the identities of symmetry for the Bernoulli polynomials arise from the study of Gauss’s multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iterated Volkenborn integral, we derive serval identities of symmetry related to the q-extension power sums and the higher order q-Bernoulli polynomials. Many previous results are special cases of the results presented in this paper, including Tuenter’s classical results on the symmetry relation between the power sum polynomials and the Bernoulli numbers in [A symmetry of power sum polynomials and Bernoulli numbers, Amer. Math. Monthly 108 (2001), no. 3, 258–261] and D. S. Kim’s eight basic identities of symmetry in three variables related to the q-analogue power sums and the q-Bernoulli polynomials in [Identities of symmetry for q-Bernoulli polynomials, Comput. Math. Appl. 60 (2010), no. 8, 2350–2359]. 2010 MSC. 11B68, 11S80. Some general families of Hurwitz-Lerch Zeta functions and their applications H. M. Srivastava Department of Mathematics and Statistics, University of Victoria Victoria, British Columbia V8W 3R4, Canada E-Mail: [email protected] Our main purpose in this lecture is to introduce and investigate the various properties of some novel families of the so-called λ-generalized Hurwitz-Lerch zeta functions. We 103 first present here many potentially useful results involving some of these λ-generalized Hurwitz-Lerch zeta functions including (for example) their partial differential equations, new series and Mellin-Barnes type contour integral representations (which are associated with Fox’s H-function) and several other summation formulas involving them. We then propose to discuss their potential application in Number Theory by appropriately constructing a presumably new continuous analogue of Lippert’s Hurwitz measure and also consider some other statistical applications of these families of the λ-generalized Hurwitz-Lerch zeta functions in probability distribution theory. A brief survey of some recent develop- ments in the subject of our presentation here will also be given. 2010 MSC. Primary 11M06, 11M35, 33B15; Secondary 11B68, 33C65, 33C90. Some families of extended Pochhammer symbols and their applications involving hyergeometric generating functions Rekha Srivastava Department of Mathematics and Statistics, University of Victoria Victoria, British Columbia V8W 3R4, Canada E-Mail: [email protected] Ever since the year 2012 when H. M. Srivastava et al. introduced and initiated the study of many interesting fundamental properties and characteristics of a certain pair of potentially useful families of the so-called generalized incomplete hypergeometric func- tions, there have appeared many closely-related works dealing substantially with notable developments involving various classes of generalized hypergeometric functions and gen- eralized hypergeometric polynomials, which are defined by means of the corresponding incomplete and other novel extensions of the familiar Pochhammer symbol. Here, in this talk, we aim at presenting a survey and investigation of some of these recent de- velopments involving several general families of hypergeometric generating functions by applying (for example) some such combinatorial identities as Gould’s identity, which stem essentially from the Lagrange expansion theorem. We also indicate various (known or new) special cases and consequences of the results presented in this paper. 2010 MSC. Primary 33B15, 33B20, 33C05, 33C15, 33C20; Secondary 33B99, 33C99. 104 Extremal problems for close-to-convex functions Toshiyuki Sugawa Graduate School of Information Sciences, Tohoku University Sendai 980-8579 Japan E-Mail: [email protected] Let S be the class of univalent analytic functions f(z) on the unit disk |z| < 1 in the complex plane normalized so that f(0) = 0 and f 0(0) = 1. Various subclasses of S have been studied. For instance, the class S∗ of starlike functions (with respect to the origin) and that K of convex functions. Another important class is that of close-to- convex functions, denoted by C. This is situated between S∗ and S; namely, S∗ ⊂ C ⊂ S. There are several geometric characterizations of close-to-convex functions. However, it is not necessarily easy to determine whether a given function f ∈ S belongs to C or not. To distinguish close-to-convex functions by its range, we will consider in this talk the quantity f(z) f(z) Φ(f; b) = inf log + b arg |z|<1 z z for a fixed real number b. In particular, we will determine the infima of Φ(f; b) over f ∈ S and f ∈ C. This is joint work with Li-Mei Wang. 2010 MSC. Primary 30C45; Secondary 30C75. Hyperbolic Fg(p; q; s) and Fφ(p; q; s) classes Luis Manuel Tovar Departamento de Matematicas, Escuela Superior de Fisica y Matematicas Instituto Politecnico Nacional, Mexico E-Mail: [email protected] We introduce the hyperbolic Fg(p; q; s) and Fφ(p; q; s) classes of holomorphic functions defined in the unit disk of C, with the aim of generalizing previous works like [Zha1] and [Li]. We give some interesting properties and characterizations in terms of other weighted hyperbolic classes. Besides we define a metric in such way that these classes result a 105 complete metric spaces. References [Zha1] . Zhao, On a general family of function spaces. Ann. Acad. Sci. Fenn. Math. Diss. No. 105. Helsinki 1996. [Li] . Li, On hyperbolic Q classes. Ann. Acad. Sci. Fenn. Math. Diss. No. 145. Helsinki 2005. 2010 MSC. Primary 30H25; Secondary 30D50. Five patterns of terminating summation formulas 3F2 Xiaoxia Wang Department of Mathematics, Shanghai University Shanghai 200444, Peoples Republic of China E-Mail: [email protected] Inspired by Chu and Wang’s recent work, who applied Gould-Hsu inversion tech- nique to establish several Whipple-like formulas of 3F2-series by investigating the dual relations of Dougall’s sum for 5F4-series, the author found five patterns of terminating 3F2 summation formulas, and the formulas contained all the results in Chu and Wang’s paper. 2010 MSC. Primary 33C20; Secondary 05A19. Bifurcation of numerical discretization in a complex amplitude equation with delayed feedback Yuanyuan Wang College of Science, China University of Petroleum (East China) Qingdao 266555, P. R. China 106 E-Mail: [email protected] In this article, we consider a complex amplitude equation with delayed feedback. The original model is translated to a two-dimensional system. Through the Euler method we study the dynamics of this resulting system. The stability of the equilibrium of the model is investigated by analyzing the characteristic equation. In the two-dimensional discrete model, we find that there are stability switches on the time delay and Hopf bifurcation when the delay passes a sequence of critical values. Finally, computer simulations are performed to illustrate the theoretical results. 2010 MSC. Primary 34K18, 74G15; Secondary 65P30 A new approximating scheme for solving fixed point problem and bilevel mixed equilibrium problem in Hilbert spaces Kriengsak Wattanawitoon∗ Department of Mathematics and Statistics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Tak, Thailand, 63000 E-Mail: [email protected] Uamporn Witthayarat Department of Mathematics, Faculty of Science, University of Phayao, Thailand, 56000 E-Mail: [email protected] In this research, we focus on the result in convergence analysis of the iterative approx- imating scheme for solving fixed point problems and bilevel mixed equilibrium problem in the framework of Hilbert Spaces. Our result extend and improve some recent results in this field. Iterative algorithm for Solving Fixed Point Problem and Bilevel 107 Generalized Mixed Equilibrium Problem in Banach Space Uamporn Witthayarat∗ Department of Mathematics, Faculty of Science, University of Phayao, Phayao, Thailand, 56000 E-Mail: [email protected] Kriengsak Wattanawitoon Department of Mathematics and Statistics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Tak, Thailand, 63000 E-Mail: [email protected] Poom Kumam Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand, 10140 E-Mail: [email protected] In this research, we study the iterative sequence for solving fixed point problem and bilevel generalized mixed equilibrium problem in a framework of real Banach space. By using auxiliary principle, the convergence theorem are proved under some mild condi- tions. Our result extend and improve some recent results in this field. On the stability of the functional equation in modular spaces Kittipong Wongkum, Parin Chaipunya, Poom Kumam Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) 126 Pracha Uthit Rd., Bang Mod, Thrung Khru, Bangkok 10140, Thailand E-Mail: [email protected]; [email protected]; [email protected] In this paper, we will investigate and present a fixed point to prove the stability of the functional equation in modular spaces. 108 Sensitivity functions in conditional convex optimization problem Gyungsoo Woo, Robert V. Namm∗, and Svetlana V. Anosova Department of Mathematics, Changwon National University, Republic of Korea Computing Center of Far Eastern Branch Russian Academy of Science, Russia Khabarovsk Infocommunications Institute of Siberian State University of Telecommunications and Informatics, Russia E-Mail: [email protected]; [email protected]; [email protected] Lagrange multiplier method based on modified Lagrangian functions is one of the main methods for solving of finite-dimensional convex optimization problem. Recently the Lagrange multiplier method is successfully applied to the solution of infinite-dimensional variational inequalities in mechanics. Convergence of Lagrange multiplier method is provided with the help of property of lower semicontinuity function in many respects. Based on condition of lower semicontinuity of sensitivity function. It is possible to prove the continuous differentiability of dual function. It allows for the solution of a dual problem to apply effective gradient methods of maximizing. In our paper we investigate the Lagrange multiplier method in finite-dimensional convex optimization problem and in infinite-dimensional semicoercive Signorini’s problem of mechanics. 2010 MSC. Primary 65K10, 65F10; Secondary 74G15, 49M15. Implicit solution function and least-norm time-stepping scheme for Z-matrix linear complementarity systems Shuhuang Xiang Department of Applied Mathematics, Central South University, Changsha, Hunan, China E-Mail: We propose a generalized Newton method for solving the system of nonlinear equations with linear complementarity constraints in the implicit or semi-implicit time-stepping 109 scheme for differential linear complementarity systems (DLCS).We choose a specific so- lution from the solution set of the linear complementarity constraints to define a lo- cally Lipschitz continuous right-hand-side function in the differential equation. More- over,wepresent a simple formula to compute an element in the Clarke generalized Jaco- bian of the solution function.We show that the implicit or semi-implicit time-stepping scheme using the generalized Newton method can be applied to a class of DLCS includ- ing the nondegenerate matrix DLCS and hidden Z-matrix DLCS, and has a superlinear convergence rate. To illustrate our approachwe consider the least element time-stepping method for simulation of linear networks with ideal switches for a class of LCSs. This is a joint work with Professor Xiaojun Chen and Mr. Yang Zhou at The Hong Kong Polytechnic University. Some normal criteria for families of meromorphic functions Bing Xiao School of Mathematical Sciences, Xinjiang Normal University Urumqi 830054, Peoples Republic of China Qifeng Wu Shaozhou Normal College, Shaoguan University Shaoguan 512009, Peoples Republic of China Weiling Xiong Department of Information and Computing Science, Guangxi University of Technology Liuzhou 545006, Peoples Republic of China E-Mail: [email protected] In this talk, we study the normality of families of meromorphic functions related a Hayman Conjecture. We consider whether a family meromorphic functions F is normal in D, if for each function f in F, f 0 + af n = b has at most one zero, where n is a positive integer, a and b 6= 0 are two finite complex numbers. Some examples show that the conditions in our results are best possible. 2010 MSC. Primary 30D35; Secondary 30D45. 110 Fixed point theorems for new generalized nonlinear contraction mappings in multiplicative metric spaces Oratai Yamaod and Wutiphol Sintunavarat Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani 12121, Thailand. E-Mail: oratai [email protected]; [email protected] In this talk, we establish fixed point theorems for new generalized nonlinear contrac- tion mappings in multiplicative metric spaces. Our results substantially generalize and .. .. improve the recent result of Ozavsar and Cevikel [M. Ozavsar, AC. Cevikel, Fixed point of multiplicative contraction mappings on multiplicative metric space. arXiv: 1025.5131v1 [matn.GN] (2012)]. 2010 MSC. 47H09; 47H10. 111 Weil-Petersson metric on square integrable Teichm¨uller spaces Masahiro Yanagishita Departments in Fundamental Science and Engineering, Waseda University, Research Fellow of Japan Society for the Promotion of Science 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan E-Mail: [email protected] The square integrable Teichm¨ullerspace is the subspace of the Teichm¨ullerspace composed of Teichm¨ullerequivalence classes with a square integrable Beltrami coefficient. The Weil-Petersson metric is a hermitian metric defined canonically on finite dimensional Teichm¨ullerspaces. In this talk, we define a hermitian metric corresponding to the Weil- Petersson metric on square integrable Teichm¨ullerspaces, and show its K¨ahlerity. 2010 MSC. Primary 30F60; Secondary 32G15, 58B20. Compact linear combinations of composition operators induced by linear fractional maps Jongho Yang∗, Boo Rim Choe, Hyungwoon Koo Department of Mathematics, Korea University Seoul 136-713, Republic of Korea E-Mail: [email protected]; [email protected]; [email protected] Maofa Wang School of Mathematics and Statistics, Wuhan University, Wuhan, China E-Mail: [email protected] It has been known that the difference of two composition operators induced by linear fractional self-maps of a ball cannot be nontrivially compact on either the Hardy space or any standard weighted Bergman space. In this paper we extend this result in two significant directions: the difference is extended to general linear combinations and in- ducing maps are extended to linear fractional maps taking a ball into another possibly of different dimension. 112 2010 MSC. Primary 47B33; Secondary 32A35, 32A36. Stronger uncertainty principles for quaternion Fourier transforms Yan Yang School of Mathematics and Computational Science, Sun Yat-Sen University Guangzhou, China E-Mail: [email protected] The quaternion Fourier transform has been widely used to analyze color images in different applications. The use of a quaternion representation allows the analysis of a color image as a vector field. In this paper, the quaternion Fourier transform and its properties are reviewed. Using the polar form of quaternion signals, we prove two stronger uncertainty principles associated with covariance and absolute covariance for the (right-sided) quaternion Fourier transform. The results generalize the classical un- certainty principle (with covariance) and the latest results about uncertainty principle (with absolute covariance) to the 2D space. Several examples are presented. 2010 MSC. Primary 46F10, 30G35. On geodesic geometry in (asymptotic) Teichm¨ullerspaces Guowu Yao Department of Mathematical Sciences, Tsinghua University Beijing 100084, People’s Republic of China E-Mail: [email protected] 113 We will introduce the situation on the geodesics and geodesic disks in the Teichm¨uller space and present some new results on the geodesic geometry in an infinite-dimensional asymptotic Teichm¨ullerspace. 2010 MSC. Primary 30C75, 30C62. The split common fixed point problem for the pseudo-contractive and quasi-nonexpansive mappings Yonghong Yao Department of Mathematics, Tianjin University Tianjin 300387, China E-Mail: [email protected] In this talk, we study the split common fixed point problem which is to find a fixed point of a pseudo-contractive mapping in one space whose image under a linear trans- formation is a fixed point of a quasi-nonexpansive mapping in the image space. We formulate and analyze an iterative algorithm for solving this split common fixed point problem. Weak convergence theorem is given. 2010 MSC. Primary 49J53, 49M37;; Secondary 65K10, 90C25. Several recent results regarding the meromorphic solutions of some algebraic differential equations and its applications Wenjun Yuan, Zifeng Huang, Maozhun Fu School of Mathematics and Information Sciences, Guangzhou University Guangzhou 510006, Peoples Republic of China Jianming Qi Department of Mathematics and Physics, Shanghai Dianji University 114 Shanghai 201306, Peoples Republic of China E-Mail: [email protected] In this talk, we introduce several recent results with respect to the integrality and exact solutions of some algebraic differential equation and its applications. We obtain the sufficient and necessary conditions of integrable and the general meromorphic solutions of these equations by the complex method, which improves the corresponding results obtained by many authors. All traveling wave exact solutions of many non-linear partial differential equations are obtained by making use of our results. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics. 2010 MSC. Primary 34A05, 30D35; Secondary 34A20, 30D45. The general traveling wave solutions of the Fisher type equations and some related problems Wenjun Yuan School of Mathematics and Information Sciences, Guangzhou University Guangzhou 510006, Peoples Republic of China Bing Xiao School of Mathematical Sciences, Xinjiang Normal University Urumqi 830054, Peoples Republic of China Yonghong Wu Department of Mathematics and Statistics, Curtin University of Technology GPO Box U 1987, Perht WA 6845, Australia E-Mail: [email protected] In this talk, we introduce two recent results with respect to the integrality and exact solutions of the Fisher type equations and its applications. We obtain the sufficient and necessary conditions of integrable and the general meromorphic solutions of these equations by the complex method, which improves the corresponding results obtained by many authors. All traveling wave exact solutions of many non-linear partial differential 115 equations are obtained by making use of our results. Furthermore, some related open problems are proposed. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics. 2010 MSC. Primary 34A05, 30D35; Secondary 34A20, 30D45. Entire solutions of certain class of differential-difference equations Fengrong Zhang∗, Nana Liu, Weiran L¨u College of Science, China University of Petroleum, Qingdao 266555, P. R. China and Chungchun Yang Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China E-Mail: [email protected]; [email protected] As a continuation of our previous studies, we will discuss the transcendental entire solutions of the following type of differential-difference equation 3 0 (k) α1z α2z f (z) + P1(z, ∆f, ··· , f , ··· , f ) = λ1e + λ2e , (k) where P1 is a linear polynomial in f, ∆f, ··· , f , with polynomials as the coefficients, and λ1, λ2, α1, α2 ∈ C are nonzero constants such that α1 6= α2. 2010 MSC. Primary 11M06, 42A16; Secondary 11B68, 11Y60. C∞-Solutions for the p-order Feigenbaum’s functional equation h(g(x)) = gp(h(x)) Min Zhang College of Science, China University of Petroleum Qingdao 266580, Shandong, People’s Republic of China 116 E-Mail: [email protected] This work deals with the Feigenbaum’s functional equation h(g(x)) = gp(h(x)), g(0) = 1, 0 ≤ g(x) ≤ 1, x ∈ [0, 1], where p ≥ 2 is an integer, gp is the p-fold iteration of g, and h(x) is strictly increase continuous function on [0, 1] that satisfies h(0) = 0, h(x) < x, (x ∈ (0, 1]). Using the constructive method, we discuss the existence of C∞-single-valley solutions of the above equation. 2010 MSC. 39B12, 34K05.