Convergence theorem for solving generalized mixed equilibrium problem and finding fixed point of a weak Bregman relatively nonexpansive mapping in Banach spaces

TL;DR

This paper introduces a new iterative method to find fixed points of weak Bregman relatively nonexpansive mappings and solutions to generalized mixed equilibrium problems in Banach spaces, advancing the theoretical understanding of these problems.

Contribution

The paper presents a novel convergence theorem for an iterative method addressing generalized mixed equilibrium problems and fixed points in Banach spaces.

Findings

Established convergence of the proposed iterative method.

Extended fixed point theory to weak Bregman relatively nonexpansive mappings.

Provided conditions ensuring solution existence.

Abstract

In this paper, we study a new iterative method for finding the fixed point of a weak Bregman relatively nonexpansive mapping and the set of solutions of generalized mixed equilibrium problems in Banach spaces.