TY - JOUR

T1 - On split feasibility problem for finite families of equilibrium and fixed point problems in Banach spaces

AU - Abass, Hammed A.

AU - Oyewole, Olawale K.

AU - Mebawondu, Akindele A.

AU - Aremu, Kazeem O.

AU - Narain, Ojen K.

N1 - Funding Information:
Hammed A. Abass acknowledges with thanks the bursary and financial support from the Department of Science and Technology and the National Research Foundation of the Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF CoE-MaSS) Post-doctoral Bursary. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS.
Publisher Copyright:
© 2022 Hammed A. Abass et al., published by De Gruyter.

PY - 2022/1/1

Y1 - 2022/1/1

N2 - In this article, motivated by the works of Ali Akbar and Elahe Shahrosvand [Split equality common null point problem for Bregman quasi-nonexpansive mappings, Filomat 32 (2018), no. 11, 3917-3932], Eskandani et al. [A hybrid extragradient method for solving pseudomonotone equilibrium problem using Bregman distance, J. Fixed Point Theory Appl. 20 (2018), 132], B. Ali and M. H. Harbau [Convergence theorems for Bregman K-mappings and mixed equilibrium problems in reflexive Banach spaces, J. Funct. Spaces (2016) Article ID 5161682, 18 pages], and some other related results in the literature, we introduce a hybrid extragradient iterative algorithm that employs a Bregman distance approach for approximating a split feasibility problem for a finite family of equilibrium problems involving pseudomonotone bifunctions and fixed point problems for a finite family of Bregman quasi-Asymptotically nonexpansive mappings using the concept of Bregman K-mapping in reflexive Banach spaces. Using our iterative algorithm, we state and prove a strong convergence result for approximating a common solution to the aforementioned problems. Furthermore, we give an application of our main result to variational inequalities and also report a numerical example to illustrate the convergence of our method. The result presented in this article extends and complements many related results in the literature.

AB - In this article, motivated by the works of Ali Akbar and Elahe Shahrosvand [Split equality common null point problem for Bregman quasi-nonexpansive mappings, Filomat 32 (2018), no. 11, 3917-3932], Eskandani et al. [A hybrid extragradient method for solving pseudomonotone equilibrium problem using Bregman distance, J. Fixed Point Theory Appl. 20 (2018), 132], B. Ali and M. H. Harbau [Convergence theorems for Bregman K-mappings and mixed equilibrium problems in reflexive Banach spaces, J. Funct. Spaces (2016) Article ID 5161682, 18 pages], and some other related results in the literature, we introduce a hybrid extragradient iterative algorithm that employs a Bregman distance approach for approximating a split feasibility problem for a finite family of equilibrium problems involving pseudomonotone bifunctions and fixed point problems for a finite family of Bregman quasi-Asymptotically nonexpansive mappings using the concept of Bregman K-mapping in reflexive Banach spaces. Using our iterative algorithm, we state and prove a strong convergence result for approximating a common solution to the aforementioned problems. Furthermore, we give an application of our main result to variational inequalities and also report a numerical example to illustrate the convergence of our method. The result presented in this article extends and complements many related results in the literature.

KW - Bregman quasi-nonexpansive

KW - equilibrium problem

KW - fixed point problem

KW - iterative scheme

KW - pseudomonotone operators

UR - http://www.scopus.com/inward/record.url?scp=85140299754&partnerID=8YFLogxK

U2 - 10.1515/dema-2022-0158

DO - 10.1515/dema-2022-0158

M3 - Article

AN - SCOPUS:85140299754

VL - 55

SP - 658

EP - 675

JO - Demonstratio Mathematica

JF - Demonstratio Mathematica

SN - 0420-1213

IS - 1

ER -