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 - 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

SN - 0420-1213

VL - 55

SP - 658

EP - 675

JO - Demonstratio Mathematica

JF - Demonstratio Mathematica

IS - 1

ER -