UNIVERSITY OF

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- Lacunary Ces풂ro 퐶,1.1 -Statistical Convergence of Difference Double Sequences Abstract:- Recently, Esi [2] defined the statistical analogue for double difference sequences 푥 = (푥푘,푙) as follows: A double sequence 푥 = (푥푘,푙) is said to be 푃 -statistically ∆ -convergent to 퐿 provided for each 휀 > 0 1 푃 – lim { 푡h푒 푛푢푚푏푒푟 표푓 (푘, 푙): 푘 < 푚, 푙 < 푛, | ∆푥푘,푙 – L | ≥ 휀 } = 0 푚,푛 푚푛 Using this definition, Esi [2] introduced and studied lacunary statistical convergence for difference double sequences and also gave some inclusion theorems. In this paper we in analogy to Esi, defined and proved some inclusion theorems for lacunary Ces푎ro 퐶,1.1 - Statistical convergence of difference double sequences.

Impact Factor:- 3.97

Researchers Name(s):- A. M. Brono (Lead Researcher First) Researchers Address(es):- Mathematics and Statistics Department, University of Maiduguri, , Correspondance Address:- Mathematics and Statistics Department, University of Maiduguri, Borno (Tel. No., Email, Physical) State, Nigeria 08032356905. [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- IOSR Journal of Mathematics (IOSR-JM) (Journal) (Journal, Periodical etc, Vol. e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 12, Issue 1 Ver. , PP page Nos) 01-05 www.iosrjournals.org Year of Publication:- 2016 Source of Funding and Amount Self $ 75 (USD) ($, £, # ) $ 45 (USD) for hard copy (additional)

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- NONLINEAR PROGRAMMING: THE PATH – FOLLOWING APPROACH Abstract:- The path – following technique presented in Mohammed and Bassi (2014) is applied to nonlinear programming problems (NLP). Since path following applies most easily to equations, and since the K-T conditions possess inequalities, and the resultant kinks could make our path following quite cumbersome, first we eliminate the inequalities in the K-T conditions and form the K-T equations. The K-T equations have only equalities and are smooth, and permits us to easily path follow- The K-T equations and the K-T conditions are equivalent and are necessary and sufficient for 푥∗ to be optimal for the NLP problem. Next, by adding a parameter t, a path is created, that path being the optimal solutions to the dynamic nonlinear programming as t varied. We finally use the dynamic nonlinear programming NLP to develop a path – following algorithm for the NLP itself. This paper is quite fundamental, and indeed its concepts provide the foundation for the equilibrium programming problems. Impact Factor:-

Researchers Name(s):- M. Abdullahi and A. M. Brono (Lead Researcher First) Researchers Mathematics and Statistics Department, University of Maiduguri, Borno Address(es):- State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno Address:- State, Nigeria (Tel. No., Email, 08032356905. Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- Research Journal of Science, Volume 11, Nos. 1 & 2 (Journal, Periodical etc, Vol. page Nos) Year of Publication:- 2005

Source of Funding and # 10,000 Amount ($, £, # )

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- AN ASSESSMENT OF ROAD ACCIDENTS AND CASUALTIES IN NIGERIA FROM 1992 - 1997 Abstract:- This paper discussed the incidence of road accidents and casualties in Nigeria from 1992 – 1997. Out of a total of 99,350 cases of accidents recorded, the serious cases topped highest with 41.33%. The accident data were obtained from the Nigeria Police Headquarters, and Statistical inferences were drawn using both descriptive statistics and regression analysis. Foremost in the ranking of the accidents severity included Lagos, Edo, Ogun and Kano States. The number of fatalities inferred that there was a strong relation between the dependent and independent variables resulting to a positive correlation. In the same vein, the number fatalities/1000 accidents and number of fatalities gave a good fit. However, this research will no doubt assist in the management and policy issues relating to administrative and enforcement of safety regulations and counter measures on road accidents in this country. Impact Factor:-

Researchers Name(s):- Ali Musa Kundiri, Ahmadu Mohammed Brono and Haruna Bakari Rann (Lead Researcher First) Researchers Department of Civil and Water Resourses Engineering, University of Address(es):- Maiduguri, Borno State, Nigeria. Mathematics and Statistics Department, University of Maiduguri, Borno State, Nigeria| Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno Address:- State, Nigeria (Tel. No., Email, 08032356905. Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- Research Journal of Science, Volume 9, Nos. 1 & 2 ISSN 1119-2542

(Journal, Periodical etc, A Journal Published by the Faculty of Science. University of Maiduguri. Vol. page Nos) Nigeria. Year of Publication:- 2003 Source of Funding and # 10,000 Amount ($, £, # )

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- A note on recent developments in statistical convergence of sequences

Abstract:- One of the most recent generalizations of the concept of classical convergence of sequences is the statistical convergence. It was defined almost fifty years ago but recently it became the center of attraction for many researchers. The object of this note is to discuss fundamental concepts and results in this field along with various generalizations which have been subsequently formulated. Impact Factor:-

Researchers Name(s):- Z.U. Siddiqui , A. M. Brono , A. Kiltho (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno Address:- State, Nigeria (Tel. No., Email, 08034575844 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- Research Journal of Science 15 : 15-23 (Journal, Periodical etc, Vol. page Nos) Year of Publication:- 2008 Source of Funding and # 10, 000 Amount ($, £, # )

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- A NOTE ON GENERALIZED ABSOLUTE NÖRLUND SUMMABILITY FACTORS OF INFINITE SERIES Abstract:- Mazhar (1972) obtained the necessary and sufficient conditions for an infinite series ∑ 푎푛휀푛 to be summable |N, p| whenever the series ∑ 푎푛 is summable |푁̅̅̅ , 푞|. He used the absolute regularity of the method |N, p| to get this result. Siddiqui (1995) and Sulaiman (2004) generalized the result of Mazhar in two different ways. Siddiqui used a more generalized form of Nörlund means, while Sulaiman added a factor to the method used by Mazhar. In this paper we obtained a result which contains both the results Siddiqui and Sulaiman as special cases Impact Factor:-

Researchers Name(s):- Z.U. Siddiqui , Bhar E. B. Gi and A. M. Brono , (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno Address:- State, Nigeria (Tel. No., Email, 08034575844 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- International Journal of Mathematical Sciences, Volume 3, Number 1. (Journal, Periodical etc, Vol. page Nos) Year of Publication:- 2011 Source of Funding and # 10,000 Amount ($, £, # )

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- STATISTICAL LIMIT POINTS FOR DOUBLE SEQUENCES

Abstract:- Following the recently introduced concept of statistical cluster points for a sequence, the definition for the statistical cluster point for double sequences has been given. Also, the analogous statistical limit point theorems for sequences have been formulated for double sequences. It has been shown, in particular, that the set of statistical cluster points of a double sequence is a closed set. Further, it has been proved that if a double sequence has a nonthin subsequence then it possesses a statistical cluster point. Finally, the analogue of Heine-Borel Covering Theorem for double sequence has been obtained for statistical convergence. Impact Factor:-

Researchers Name(s):- A. M. Brono , Z.U. Siddiqui , and B. B. Gi (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno Address:- State, Nigeria (Tel. No., Email, 08032356905 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- International Journal of Mathematical and Computational Analysis, Volume (Journal, Periodical etc, 4, Number 1. Vol. page Nos) Printed in Nigeria. All Right Reserved ISSN: 2251-1067 Copyright©2012 Blackwell@Educational Books Year of Publication:- 2012 Source of Funding and # 10,000

Amount ($, £, # )

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- SOME INEQUALITIES ON STATISTICAL SUMMABILITY (C, 1.1)

Abstract:- Recently, Moricz (2000) defined the concept of statistical (C,1)-summability. A sequence = (푥푘 ) is statistically summable (C,1) to L if the sequence 훿 = (훿푘 ) of arithmetic means of the sequence x, is statistically convergent to L, 푖. 푒푠푡 − 푙푖푚훿 = 퐿. Mursaleen, Alotaibi and Mohiuddine (2008) proved some inequalities related to the concept of 퐶1(푠푡)-conservative matrices, 퐶1(푠푡)- limsup and 퐶1(푠푡)-liminf, which are natural analogues of (푐 − 푠푡 ∩ 푙∞)- matrices [cf. Kolk (1996), st.limsup and st-liminf, respectively [cf. Fridy and orhan(1997)]. Such types of inequalities are also considered by Coskum and Cakan(2005) and Cakan and Atlay (2006). Moricz(1996) defined the concept of statistical (C,1.1) summability. The space of all Cesaro summable double sequences is denoted by (C,1.1). In this paper, we prove some inequalities related to the concepts of (C,1.1) st-conservatives matrices, C,1.1(st)-limsup, and C,1.1(st)-liminf, which are natural analogues of 퐶1(푠푡)-conservative matrices, 퐶1(푠푡)-limsup and 퐶1(푠푡)-liminf, respectively. Impact Factor:-

Researchers Name(s):- A. M. Brono , Z.U. Siddiqui , and B. A. Madu (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno Address:- State, Nigeria (Tel. No., Email, 08032356905 Physical) [email protected]

Publication Status:- Published (published/unpublished) Source of Publication:- Nigerian Mathematical Society (Journal, Periodical etc, 31st Annual Conference Vol. page Nos) Year of Publication:- 2012 Source of Funding and # 10,000 Amount ($, £, # )

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- CESÁRO STATISTICAL CORE OF DOUBLE SEQUENCES

Abstract:- In this paper, Cesáro statistical core Of double sequences have been obtained. The concept of RH regularity of four dimensional matrices in Pringsheim’s sense has been used to find the analogues of the results for statistical core of sequences. Impact Factor:- 2.75

Researchers Name(s):- Z.U. Siddiqui , A. M. Brono , A. Kiltho (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno Address:- State, Nigeria (Tel. No., Email, 08034575844, Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- Far East Journal of Mathematical Sciences (FJMS) Volume 69, number 2, (Journal, Periodical etc, Pages 261-274 Vol. page Nos) Year of Publication:- 2012 Source of Funding and Self $ 560 (USD) Amount ($, £, # )

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM Research Title:- Generalised Statistical Convergence For Double Sequences Abstract:- Recently, the concept of 훽-statistical Convergence was introduced considering a sequence of infinite matrices 훽 = (bnk(푖) ). Later, it was used to define and study 훽-statistical limit point, 훽-statistical cluster point, stβ- 푙푖푚푖푡 inferior and stβ- 푙i푚푖푡 superior. In this paper we analogously define and study 2훽-statistical limit, 2훽-statistical cluster point, st2β- 푙푖푚푖푡 inferior and st2β- 푙푖푚푖푡 superior. for double sequences Impact Factor:- 3.97

Researchers Name(s):- A. M. Brono , Z.U. Siddiqui (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno Address:- State, Nigeria (Tel. No., Email, 08032356905 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- IOSR Journal of Mathematics (IOSR-JM) (Journal, Periodical etc, e- ISSN: 2278-5728,p-ISSN: 2319-765X, volume 6, Issue 2, PP 01-04 Vol. page Nos) www.iosrjournals.org Year of Publication:- 2013 Source of Funding and Self $ 75 (USD) Amount ($, £, # ) $ 45 (USD) for hard copy (additional)

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM Research Title:- I-Cesáro Statistical Core Of Double Sequences Abstract:- The concept of statistical limit inferior and superior for single sequences was introduced by Fridy and Orhan (1997) where some inequalities and Knopp type core theorem were obtained. Cakan and Altay extended these results to double sequences, similar results were obtained for 퐶1,1(st2)-sequences by Siddiqui et al. (2012). Demirci (2001), Lahiri and Das (2003) used the same concept to define the 퐼 -limit inferior, 퐼 -limit superior and obtained some 퐼 -analogue of the properties of limit inferior and superior for single sequences. Kumar (2007) further extended this concept to double sequences. In this paper we define - 퐼 퐼 퐶,1,1 (st2)-limit inferior, superior and 퐶,1,1 (st2)-Core which are 퐼 - analogues of 퐶1,1(st2)-limit inferior, superior and 퐶1,1(st2) -Core for double sequences respectively. Impact Factor:- 3.97

Researchers Name(s):- A. M. Brono, A. G. K. Ali (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State Nigeria Department of Mathematics, Kashim Ibrahim College of Maiduguri, Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno State, Address:- Nigeria (Tel. No., Email, 08032356905 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- IOSR Journal of Mathematics (IOSR-JM) (Journal, Periodical etc, e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 13, Issue 3 Ver. 1, Vol. page Nos) PP 63-66 www.iosrjournals.org

Year of Publication:- 2017 Source of Funding and Self $ 75 (USD) Amount ($, £, # ) $ 45 (USD) for hard copy (additional)

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- I2- Statistical And I2 -Lacunary Statistical Convergence for Double Sequence of Order α Abstract:- Following the recent generalization of the recently introduced summability methods namely 퐼 -statistical convergence of order 훼 and 퐼 -lacunary statistical convergence of order 훼, where 0 < 훼 < 1; Relationships were investigated and some observations about these classes were made and answers were proffered to the open problems posed by Das, Savas and Ghosal in [10]. We shall analogously extend above notions to double sequences. Impact Factor:- 3.97

Researchers Name(s):- A. M. Brono, A. G. K. Ali And M. T. Bukar (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State Nigeria Department of Mathematics, Kashim Ibrahim College of Education Maiduguri, Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno Address:- State, Nigeria (Tel. No., Email, 08032356905 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- IOSR Journal of Mathematics (IOSR-JM) (Journal, Periodical etc, e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 13, Issue I Ver. VI,

Vol. page Nos) PP 107-112 www.iosrjournals.org Year of Publication:- 2017 Source of Funding and Self $ 75 (USD) Amount ($, £, # ) $ 45 (USD) for hard copy (additional)

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- Lacunary Arithmetic Statistical Convergence For Double Sequences.

Abstract:- This paper extends the recently introduced summability concept of convergence namely; arithmetic statistical convergence and lacunary arithmetic statistical convergence, to double sequences. We shall also investigate the relationship between these concepts and prove some inclusion theorems Impact Factor:- 3.97

Researchers Name(s):- A. M. Brono, M. M. Karagama And F. B. Ladan (Lead Researcher First) Researchers Department of Mathematical Sciences, University of Maiduguri, Borno Address(es):- State, Nigeria Correspondence Department of Mathematical Sciences, University of Maiduguri, Borno Address:- State, Nigeria (Tel. No., Email, 08032356905 Physical) Email: [email protected]

Publication Status:- Published (published/unpublished) Source of Publication:- IOSR Journal of Mathematics (IOSR-JM) (Journal, Periodical etc, e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 13, Issue 6 Ver. II,

Vol. page Nos) PP 06-11 www.iosrjournals.org Year of Publication:- 2017 Source of Funding and Self $ 75 (USD) Amount ($, £, # ) $ 45 (USD) for hard copy (additional)

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- On 퐼2- statistically Pre-Cauchy Double Sequences Abstract:- Following the recent introduction of the summability notion of I- statistically Pre-Cauchy double sequence, we shall in this paper introduce the notion of 퐼2- statistical cluster point for statistically Pre- Cauchy double sequence and prove some relationships between them 퐼2- statistically Pre-Cauchy double sequence and 퐼2- statistical convergence. Impact Factor:- 3.97 Researchers Name(s):- A. M. Brono, A. G. K. Ali (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State Nigeria Department of Mathematics, Kashim Ibrahim College of Education Maiduguri, Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno State, Address:- Nigeria (Tel. No., Email, 08032356905 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- IOSR Journal of Mathematics (IOSR-JM) (Journal, Periodical etc, e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 13, Issue 3 Ver. 1, Vol. page Nos) PP 63-66 www.iosrjournals.org Year of Publication:- 2017 Source of Funding and Self $ 75 (USD) Amount ($, £, # ) $ 45 (USD) for hard copy (additional)

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- Some Recent Developments On Statistical Convergence(“ A New Type of Convergence” ) And Convergence In Statistics Abstract:- One of the most recent generalizations of concept of classical convergence of sequences (“ a new type of convergence”) is statistical convergence defined by Fast. Recently, it became the centre of attraction many researchers. The objective of this review is to discuss fundamental concepts and results in statistical convergence along with various generalizations which have been subsequently formulated. And finally expose the statistics in statistical convergence. Impact Factor:- 3.97 Researchers Name(s):- A. G. K. Ali And A. M. Brono (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State Nigeria. Department of Mathematics, Kashim Ibrahim College of Education Maiduguri, Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno Address:- State, Nigeria (Tel. No., Email, 08032356905 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- IOSR Journal of Mathematics (IOSR-JM) (Journal, Periodical etc, e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 12, Issue 1 Ver. III, Vol. page Nos) PP 13-23 www.iosrjournals.org Year of Publication:- 2016 Source of Funding and Self $ 75 (USD) Amount ($, £, # ) $ 45 (USD) for hard copy (additional)

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- On Statistical Convergence of Double Sequences and Statistical Monotonicity Abstract:- Following the introduction of the concepts of statistical monotonicity and upper (or lower) peak points of real valued single sequence by Kaya et al in 2013. We shall in this paper investigate properties of statistical convergence double sequences, introduce definitions of statistical monotonicity and lower ( upper) peak points of real valued double sequence. And establish the relationship between the statistical convergence of double sequences and these notions. Finally, we generalized statistical monotonicity using an RH- regular doubly infinite matrix transformation. Impact Factor:- 3.97 Researchers Name(s):- A. M. Brono, A. G. K. Ali (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State Nigeria Department of Mathematics, Kashim Ibrahim College of Education Maiduguri, Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno State, Address:- Nigeria (Tel. No., Email, 08032356905 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- IOSR Journal of Mathematics (IOSR-JM) (Journal, Periodical etc, e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 12, Issue 1 Ver. III, Vol. page Nos) PP 45-51 www.iosrjournals.org Year of Publication:- 2016 Source of Funding and Self $ 75 (USD) Amount ($, £, # ) $ 45 (USD) for hard copy (additional)

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- 2 – Statistical Convergence in 2n-Normed Space Abstract:- The concept of -statistical convergence in n-normed space was introduced by Hazarika and Savas in[19]. They established some inclusion relations between the set of statistically convergent and - statistical convergence sequences. They also found the relation of - statistical convergence sequence to statistical convergence, (c, 1)- summability and strong (v,1)- summability in n-normed spaces. In this paper, we extend these concepts to double sequences in 2n-normed spaces. We also analogously studied and established similar relation of 2 – Statistical Convergence to (c, 1.1)-summability and strong (v, 2 )-summability in 2n-normed spaces. Impact Factor:- 2.75 Researchers Name(s):- A. M. Brono, A. G. K. Ali (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State Nigeria Department of Mathematics, Kashim Ibrahim College of Education Maiduguri, Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno State, Address:- Nigeria (Tel. No., Email, 08032356905 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- Far East Journal of Mathematical Sciences (FJMS) Volume 99, number 10, (Journal, Periodical etc, Pages 1551-1569 Vol. page Nos) Year of Publication:- 2016 Source of Funding and Self $ 800 (USD) Amount ($, £, # )

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- A Matrix Characterisation of Cesáro 퐶,1.1 -Statistically Convergent Double Sequences. Abstract:- Fridy and Miller [7] gave a characterisation of statistical convergence for bounded single sequences using a family of matrix summability methods. Miller and Wieren [13] analogously extended and proved the results for double sequences. In this paper, we shall further prove the results for Cesáro 퐶,1.1 -Statistically Convergent Double Sequences. Impact Factor:- 2.75 Researchers Name(s):- A. M. Brono and A. G. K. Ali (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State Nigeria Department of Mathematics, Kashim Ibrahim College of Education Maiduguri, Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno State, Address:- Nigeria (Tel. No., Email, 08032356905 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- Far East Journal of Mathematical Sciences (FJMS) Volume 99, Number 11, (Journal, Periodical etc, Pages 1693-1702 Vol. page Nos) Year of Publication:- 2016 Source of Funding and Self $ 400 (USD) Amount ($, £, # )

UNIVERSITY OF MAIDUGURI

OFFICE OF THE VICE-CHANCELLOR

CENTRE FOR RESEARCH AND INNOVATION FORMAT FOR COMPILING RESEARCH COMPENDIUM

Research Title:- Weighted Cesáro 퐶,1.1 -Statistical Convergence of Double Sequences. Abstract:- Following the method of weighted statistical convergence for single sequences, we analogously define double weighted Cesáro statistical convergence and establish its relationship with Nörlund type 2 transformation (푁̅ , 훽푛) and Cesáro 퐶,1.1 -summability. Impact Factor:- 2.75 Researchers Name(s):- A. M. Brono and A. G. K. Ali (Lead Researcher First) Researchers Department of Mathematics and Statistics, University of Maiduguri, Address(es):- Borno State Nigeria Department of Mathematics, Kashim Ibrahim College of Education Maiduguri, Borno State, Nigeria Correspondance Mathematics and Statistics Department, University of Maiduguri, Borno State, Address:- Nigeria (Tel. No., Email, 08032356905 Physical) [email protected] Publication Status:- Published (published/unpublished) Source of Publication:- Far East Journal of Mathematical Sciences (FJMS) Volume 100, Number 3, (Journal, Periodical etc, Pages 361-369 Vol. page Nos) Year of Publication:- 2016 Source of Funding and Self $ 400 (USD) Amount ($, £, # )