An extragradient algorithm for split generalized equilibrium problem and the set of fixed points of quasi-φ-nonexpansive mappings in Banach spaces

Abstract

In this paper, we study the problem of finding a common solution to split generalized mixed equilibriumproblem and fixed point problem for quasi-φ-nonexpansive mappings in 2-uniformly convex and uniformly smoothBanach space E1 and a smooth, strictly convex, and reflexive Banach space $E_2$ . An iterative algorithm with Armijolinesearch rule for solving the problem is presented and its strong convergence theorem is established. The convergenceresult is obtained without using the hybrid method which is mostly used when strong convergence is desired. Finally,numerical experiments are presented to demonstrate the practicability, efficiency, and performance of our algorithm incomparison with other existing algorithms in the literature. Our results extend and improve many recent results in thisdirection.