Priyabrat Gochhayat

Sambalpur University Department of Government Email: [email protected] Jyoti Vihar, 768019, Burla, Email: [email protected] Sambalpur, , India Homepage: https://www.priyabratg.in

Experience

— Assistant Professor in , Odisha, India with effect from Nov. 2009 – till date. — Post-Doctoral Research, University of Pretoria, South Africa, with effect from Aug. 2012– July 2014 (On study leave from Sambalpur University). — Assistant Professor of Mathematics, Krupajal Engineering College, , Odisha, India, from 4th Aug. 2009 – 15th Nov. 2009. — Junior/Senior Research Fellow in a NBHM, DAE, Govt. of India sponsored research project at Berham- pur University, Odisha, India, from Dec. 2007 – Dec. 2008. — CSIR Senior Research Fellow, Govt. of India from April 2008 – July 2009.

Research Interests

I am interested in the theory univalent functions and its harmonic analogues, orthogonal polynomials on R and special functions. My current projects focusing on to investigate radii like problems, sharp bounds, maximal area integral problems of certain univalent (harmonic) mappings and to study the location and interlacing of zeros of q-polynomials.

Research

Projects Undertaken Completed the project entitled Studies on univalent and multivalent functions in the context of geometric functions theory, funded by DST, Govt. of India. (Rs. 11,52,000/-) . Past Projects Worked with Professor Kerstin Jordaan in the project entitled Location of real zeros and asymptotic zero distribution of 3F2 hypergeometric polynomials at University of Pretoria, South Africa. Worked with Professor Akshaya Kumar Mishra as a Junior/Senior Research Fellow in the NBHM, DAE, Govt. of India, funded project entitled A study of some extremal problems in geometric function theory and special functions at University, Odisha, India. Priyabrat Gochhayat 2

Students Supervised

PhD Student Pinaki Prasad Kar (2019–). Thesis title: Locations and interlacing properties of zeros of q-polynomials. Anuja Prajapati (2016–). Thesis title: Operators in geometric function theory. Bikash Kumar Chinhara (2012-2019). Thesis title: Studies on harmonic univalent mappings and its connection with minimal surfaces. M.Phil. Students Pamancha Kumar Behera (2019). Thesis title: Some aspects of log-harmonic and log-p-harmonic map- pings. Kalinga Kalyan Nayak (2018). Thesis title: Applications of orthogonal polynomials to geometric function theory. Jharanamayee Suna (2017). Thesis title: Monotonicity of zeros of orthogonal polynomials. Pritirani Sethi (2017). Thesis title: Maximal area integral problems of some subclasses of univalent functions. Pinaki Prasad Kar (2016). Thesis title: Interlacing properties of the zeros of some orthogonal and quasi- orthogonal polynomials. Anuja Prajapati (2016). Thesis title: Some aspects of operators in the geometric function theory. Rajesh Kumar Mishra (2016). Thesis title: On Bloch and Landau constants for univalent harmonic functions. Srikant Turia (2012). Thesis title: Some aspects of harmonic univalent mappings. Bijayinee Behera (2012). Thesis title: A study on coefficient bounds for inverse of some subclasses of univalent functions. Shiba Sankar Mallick (2011). Thesis title: Study on some subclasses of univalent functions.

Publications

— A. Prajapati, and P.Gochhayat, Applications of third order differential subordination and superordina- tion results associated with Struve functions, (2019) FILOMAT (Accepted) SCI — B. K. Chinhara, P.Gochhayat and S. Maharana, A subclasses of harmonic univalent mappings with restricted analytic part, Commun. Korean Math. Soc. 34(3) 841–854, (2019). SCI — B.K.Chinhara, P.Gochhayat and S. Maharana, On certain harmonic mappings with fixed coefficients, Monatshefte Für Mathematka, 190, 261–280, (2019). SCI — H.M. Srivastava, A. Prajapati, and P.Gochhayat, Applications of third order differential subordination and superordination results associated with Srivastava-Attiya operator. Appl. Math. Inf. Sci. 12(3), 469–481 (2018). — B.K.Chinhara, P.Gochhayat and A.K. Mishara, Certain subclasses of harmonic multivalent functions involving an integral operator, Int. J. Open Problems Complex Analysis, 10(3), 1–18, (2018). Priyabrat Gochhayat 3

— P.Gochhayat, Inclusion properties of certain subclass of multivalent functions defined by generalized derivative operator, Advances in Mathematics: Scientific Journal, 4(2), 221–227, (2015), ISSN 1857-8365 UDC: 517.546.3:517.983.22 — P.Gochhayat, KH Jordaan, K. Raghavendar and A. Swaminathan, Interlacing properties and bounds for zeros of 2φ1 hypergeometric and little q-Jacobi polynomials. Ramanujan J. 40(1), 45–62, (2016), (Impact Factor2013: 0.507) SCI — A. K. Mishra and P.Gochhayat, Sandwich-type theorems of some subclasses of multivalent functions defined by an adaptation to Srivastava-Attya operator. PanAmerican Math J, 23(1), 25–43, (2013) (ISSN: 1064-9735) — P.Gochhayat, Convolution properties of p-valent functions associated with a generalization of the Srivastava-Attiya operator, Journal of Complex Analysis, Volume 2013, Art. ID 676027, (2013). — P.Gochhayat, Sandwich-type theorem for class of functions defined by generalized differential opera- tor. Math. Vesnik, 64(2), pp 178–186, (2013). ISSN 0025-5165 (print), ISSN 2406-0682 (online) — P.Gochhayat, Sandwich-type theorems of some subclasses of multivalent functions defined by Dziok- Srivastava operator. Acta Universitatis Apulensis, 32, 31–47, (2012). (ISSN 1582-5329) — A. K. Mishra and P.Gochhayat, A coefficient inequality for a subclass of the Caratheodory functions defined using conical domains, Computers and Mathematics with Applications, 61(9), 2816–2820, (2011). Zbl 1221.30039 (Impact Factor2013: 1.996) SCI — A. K. Mishra and P.Gochhayat, Invariance of some subclasses of multivalent functions under a differ- integral operator. Complex Variables and Elliptic Equations, 55(7), (2010), 677–689. Zlb 1195.30028 (2013 Impact Factor: 0.650) SCI — A. K. Mishra and P.Gochhayat, Fekete-Szegö problem for a class defined by an integral operator. Kodai Journal of Mathematics, 33, 310–328, (2010). Zbl 1196.30013 (Impact Factor2013: 0.347) SCI — H. M. Srivastava, A. K. Mishra and P.Gochhayat, Certain subclasses of analytic and bi-univalent func- tions, Applied Math. Letters, 23, 1188–1192 (2010) . Zbl 1201.30020 (Impact Factor2013: 1.480) SCI (More than 300 Google citation and Top 25 Hottest article in Elsevier) — A. K. Mishra and P.Gochhayat, Fekete-Szegö problem for k-uniformly convex functions and for a class defined by the Owa-Srivastava operator. Journal of Mathematical Analysis and Applications, 347, 563–572, 2008. Zbl 1152.30012, MR2440350. (Impact Factor2013: 1.119) SCI — A. K. Mishra and P.Gochhayat, Second Hankel determinant of a class of analytic functions defined by fractional derivative. International Journal of Mathematics and Mathematical Sciences, Volume 2008, Art. ID 153280, 10 pages, (2008). Zbl 1158.30308, MR2392999 (2009b: 30025) — A. K. Mishra and P.Gochhayat, Coefficient of inverse functions in a nested class of starlike functions of positive order. Journal of Inequalities in Pure and Applied Mathematics, 7(3), Art. 94, 2006. Zbl 1182.30015, MR2257293 (2007f: 30024) http://jipm.vu.edu.au — A. K. Mishra and P.Gochhayat, Applications of the Owa-Srivastava operator to the class of k-uniformly convex functions. Fractional Calculus and Applied Analysis; An International Journal for Theory and Appli- cations, 9(4), 323–332 , 2006. Zbl 1132.30321, MR2300466 (2007k: 30019) (Impact Factor 2013: 2.974) SCI Priyabrat Gochhayat 4

Talks/Presentation in Conference/Workshop/Seminars

— Delivered series of lectures on Complex Analysis at Department of Mathematics, Central University of Odisha, India during Sept. 2-6, 2019. — Invited talk on Harmonic analogue of analytic univalent mappings in a National seminar at CTET, Bhilai, India on Dec. 22, 2018. — Invited talk on LaTeXI˙ in the National workshop on LaTeX, at Institute of Mathematics and Applica- tions, Bhubaneswar, Odisha, India, during 23-24, March, 2018. — Presented a paper entitled On harmonic univalent mappings in the International Conferences on Math- ematical Sciences and Applications (ICMSA2018), held at Guru Ghasidas Vishwavidyalaya, Bilaspur, India during February 23-25, 2018. — Presented a paper entitled Inclusion properties of certain subclasses of multivalent functions defined by gener- alized derivative operator in the International symposium of Geometric function theory and applications (GFTA2015), held at Cr. Cryil Methodius University, Ohrid, Macedonia, during 24-27, August 2015. — Presented a paper entitled On certain subclasses of multivalent functions in the International conference of Computational Methods and Functions Theory (CMFT2013), held at Shantou University, Shantou, China, during 10-14, June 2013. — Invited talk on An extension of Chebyshev Polynomials in the Department of Mathematics, , Odisha, India, during 21-22, December, 2012. — Presented a paper entitled Typically real functions and their connection to Chebyshev polynomials in the Research Seminar: Orthogonal Polynomials and Special Functions a Complex Analytic Perspective, University of Pretoria, South Africa on 12th Nov., 2012. — Presented a paper entitled Sandwich-type theorems and convolution properties of some subclasses of multi- valent functions defined by an adaptation to Srivastava-Attiya operator in the Annual conference of South African Mathematical Society, held at University of Stellenbosch, South Africa during 30th Oct., 2012 to 2nd Nov., 2012. — Presented a paper entitled Sandwich-type theorems of some subclasses of multivalent functions defined by Dziok-Srivastava operator in the Joint International conference of American and South African Mathe- matical Society, held at Nelson Mandela Metropolitan University, Port Elizabeth, South Africa during 28th Nov, 2011 to 2nd Dec.2011. — Presented a paper entitled Sandwich-type theorems for some subclasses of multivalent functions associated with Dziok-Srivastava operator in National seminar on Advances in complex analysis and special func- tions, Central university of Rajasthan, held, during March 12-13, 2011. — Presented a paper entitled Sandwich-type theorems for some subclasses of multivalent functions associated with differential operator in ICM2010, Hyderabad, held, during August 19-27, 2010. — Presented a paper entitled Sandwich-type theorems of some subclasses of multivalent functions defined by Dziok-Srivastava operator in the 36th Annual Conference of Orissa Mathematical Society, held at Institute of Mathematics and Applications, Bhubaneswar, Orissa, India, during February 08-09, 2009. — Presented a paper entitled Sandwich-type theorem for a class of functions defined by generalized differential operator in Pre-ICM International Convention on Mathematical Science, held at University of Delhi, during December 18-20, 2008. — Presented a paper entitled Certain Subclasses of Bi-univalent functions in the 35th Annual Conference of Priyabrat Gochhayat 5

Orissa Mathematical Society, held at Sailavala Women’s College, Cuttack,Odisha, India during Febru- ary 02-03, 2008. — Presented a paper entitled Fekete-Szegö inequality for a class defined by fractional derivative in the Interna- tional Conference on Special functions and Applications, held at MNIT, Jaipur, India, during December 15-16, 2007. — Presented a paper entitled A coefficient inequality for k-uniformly convex functions in the 34th Annual Conference of Orissa Mathematical Society, held at , , Odisha, India, during January, 28-29, 2007. — Presented a paper entitled On certain subclass of analytic functions defined by fractional derivativesI˙ in the National Conference on Mathematical Analysis and its Applications in Real-World Problems, held at Berhampur University during September, 16-17, 2006. — Presented a paper entitled Applications of certain fractional differential operator to a class of k-uniformly con- vex functions in the National Seminar on Analysis and Application, organized by Dept. of Mathematics, , Vani Vihar,Odisha, India during March 30-31, 2006. — Presented a paper entitled Applications of certain fractional differential operator to a class of k-uniformly convex functions in the International Conference on Geometric Function Theory, Special Functions and Applications, held at Pondicherry during January 02-05, 2006. — Presented a paper entitled Coefficient of inverse functions in a nested class of starlike functions of positive order at the XII-Ramanujan Symposium on Recent Trend in Analysis, held at Ramanujan Institute for Advance Study in Mathematics, University of Madras, India during March 02-04, 2005. — Presented a paper entitled Coefficient of inverse functions in a nested class of starlike functions of positive order in the 32nd Annual Conference of Orissa Mathematical Society and National Conference on Mathematical Analysis and Applications, held at NIST, Berhampur, Odisha, India during February 05-06, 2005.

Workshop/Special Training

— Participated in TEQIP sponsored workshop on Mathematica as a teaching aid, at IIT Roorkee, India, during June 10–14, 2019. — 1st International course on Orthogonal Polynomials and Special Functions: from one to several variables, at Anand-ICE, Jaipur, Rajasthan, India during March 5-7, 2019. — Refresher Course, at HRDC, Devi Ahilya Vishwavidyalaya, Indore, M.P., India, during 27th July 2018 to 16th Aug. 2018. — Orientation Course, at HRDC, Sambalpur University, Orissa, India, during 3rd Nov. 2016 to 30th Nov. 2016. — School and workshop in Complex Analysis, Geometry and Dynamics, at ICTP, Trieste, Italy, during 21st Sept. 2015 to 3rd Oct. 2015. — Instructional schools for lecturers on Real analysis and measure theoryI˙ at University of Delhi, during 26th Mar. 2012 to 7th Apr. 2012. — MTTS program at RIE, Mysore as tutor during 17th May 2010 to 12th June 2010. — Refresher Course on Mathematics and Statistics, at Sambalpur University, Orissa, India, during 4–24 Feb. 2010. Priyabrat Gochhayat 6

— International workshop on Harmonic Mappings and Hyperbolic Metrics, at IIT Madras, Chennai, during 10–19 Dec. 2009. — Advanced Instructional School in Complex AnalysisI˙ held at Bhaskaracharya Pratisthana, Pune, during 5th June 2008 to 2nd July 2008. — CMFT Workshop on Complex Analysis, held at DBI, Kharguli, Guwahati, and Organized by IASST, Guwa- hati, Assam, during 03-10, Jan. 2008. — Advanced Training Program for Lecturer in Multivariable Calculus held at University of Pune during November 6-18, 2006. — National Workshop on Graph Theory and Applications, held at NERIST, Nirjuli, Itanager, Arunachal Pradesh during 09-16, October 2006.

Education

Ph.D. Mathematics, Berhampur University, Odisha, India, 2007 – 2009. –Thesis: A study on geometric functions theory: Subclasses of univalent and multivalent functions. M.Phil. Mathematics, Berhampur University, Odisha, India, 2002 – 2003. –Dissertation: Coefficient estimate for the inverse of univalent functions. M.Sc. Mathematics, G.M.(Autonomous) College, Sambalpur University, Odisha, India, 1999 – 2001. –Project: A short review on tree. B.Sc. Mathematics Honors, U. N. College of Sc. and Tech., Utkal University, Odisha, India, 1996–1999. Post Graduate Diploma in Computer Applications (PGDCA): (2002), Bright Computer , Cut- tack Centre, Odisha, India.

Skills

Operating System: Windows XP, Window 8, Linux. Office Applications S/W: Word, Excel, Power Point, and LaTeX, R, Mathematica 9. Languages: Fortran, Pascal, C and C++.

Affiliation/ Recognition

Membership Member of Research Group in Mathematical Inequality and Applications (RGMIA), Australia. Life Member of Orissa Mathematical Society, Orissa, India. Life Member of Indian Mathematical Society, India (L/2019/17) Annual member of American Mathematical Society. Annual Member of Allahabad Mathematical Society. Priyabrat Gochhayat 7

Distinction and Award Post-Doctoral Research Fellowship, University of Pretoria, South Africa, with effect from Aug. 2012– July 2014. CSIR Senior Research Fellowship, Govt. of India from April 2008 – July 2009. 43rd foundation day award for outstanding research publication in 2008 of the Berhampur Uni- versity. Professor Ghanasyam Samal memorial award for Best Paper Presentations on 34th Annual Con- ference of Orissa Mathematical Society in 2007. 42nd foundation day award for outstanding research publication in 2007 of the Berhampur Uni- versity. Selected for 41st foundation day award for outstanding research publication in 2006 of the Berham- pur University.

Journal Referee / review

I am enjoying the service of referee and/or review of various manuscripts. Some of them are below: — American Mathematical Society Review — Mathematical and Computer Modeling — Tamkang Journal of Mathematics — Matematick Vesnik — Mathematica Slovaca — The Bulletin of the Belgian Mathematical society: Simon Stevin — Libertas Mathematica — Journal of Mathematics and Applications — Journal of Constructive Approximation. — Turkish Math. J — Hacettepe Journal of Mathematics and Statistics — Journal of Advanced Engineering and Computation (JAEC). — Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas — Bulletin of Malaysian Mathematical Society — TWMS J. App. Eng. Math. — Pure and Applied Mathematics Journal, (Editorial member) — International Journal of Mathematics Trends and Technology, (Editorial member) — Open Journal of Optimization — Communication in Korean Mathematical Society Priyabrat Gochhayat 8

Profiles

Fathers’ Name: Late Pramod Kumar Gochhayat Mothers’ Name: Shantilata Gochhayat Marital Status: Married Date of Birth: 22nd May, 1979 Nationality: Indian Religion: Hindu Category: General/SEBC Languages Known: English, Oriya and Hindi. Permanent Address : Barahipur, Adaspur, Cuttack, 754010, Odisha, India

Administrative Responsibilities

— Library in charge, Department of Mathematics, Sambalpur Univeristy since May 2015 to till date — Assistant Teacher-in-charge examinations, Department of Mathematics, Sambalpur Univeristy since Aug. 2018 to till date — Zone Supervisor, +3 Second university examinations all Arts, Science and Commerce 2019. — Zone Supervisor, +3 Second university examinations Science and Commerce 2018. — Coordinator, NSS Bureau, Sambalpur University, since November 2014 to July 2017 — Deputy center superintendent of PG Entrance Test (Mathematics), 2016. — Member of board of studies in NSS during 2014-15 — Chairman, Board of studied in the course in NSS under CBCS 2015 — Associate Vice-President of Students’ Aid Fund during 2011-12. — Member of board of studies in Mathematics, during 2011-12. — Member of e-Gov Cell for PG Admission during 2011-12. — Assistant Superintendent, 3rd Boys Hostel June 2010-May 2012. — Teacher-in-Charge of examinations, Dept. of Mathematics, Sambalpur University, 2010-2012. — NSS program officer, PG Boys’ Unit, Sambalpur University during 2010-2011.

References:

Professor Akshaya Kumar Mishra Retd. Professor of Mathematics (Berhampur University, Odisha, India) and Ex-Director, Insti- tute of Mathematics and Applications, Odisha, India; E-mail: [email protected]; Priyabrat Gochhayat 9

Phone No.: +91-(0)9861017102; +91-(0)8144160012 (M) (Professor A.K.Mishra is my M.Phil. and Ph.D supervisor, and also Principal Investigator of the major research project on which I was working.) Professor KH (Kerstin) Jordaan Department of Mathematical Sciences, University of South Africa, Pretoria E-mail: [email protected] Phone No.: +27-12 420 2788 (O), +27-(0)822999511(M) (Professor Kerstin Jordaan is my Post-Doc. Research Mentor)

Last updated: September 18, 2019