Strong convergence theorems by a new hybrid method for equilibrium problems and relatively nonexpansive mappings in Banach spaces

TL;DR

This paper introduces a new hybrid iterative method in Banach spaces to find common solutions to equilibrium problems and fixed points of relatively nonexpansive mappings, generalizing existing approaches.

Contribution

The paper proposes a novel modified Ishikawa iteration that broadens the applicability of convergence theorems in Banach spaces for equilibrium and fixed point problems.

Findings

Establishes strong convergence theorems for the new method

Generalizes previous results in the literature

Provides a framework for solving combined equilibrium and fixed point problems

Abstract

In this paper, we introduce a new modified Ishikawa iteration for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in a Banach space. Our results generalize, extend and enrich some existing results in the literature.