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

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.