Hybrid Algorithm for Nonlinear Equilibrium, Variational Inequality and Fixed Point Problems

TL;DR

This paper presents a new iterative algorithm that converges strongly to a common solution for multiple complex problems in Banach spaces, improving existing results in the field.

Contribution

It introduces a novel iterative process that unifies solutions for equilibrium, fixed point, and zero problems, extending and generalizing recent theoretical results.

Findings

Converges strongly to a common solution in Banach spaces.

Generalizes several recent results in the literature.

Provides an independent iterative method of broad applicability.

Abstract

In this paper, we introduce an iterative process which converges strongly to a common element of sets of solutions of finite family of generalized equilibrium problems, sets of fixed points of finite family of continuous relatively nonexpansive mappings and sets of zeros of finite family of $\gamma$-inverse strongly monotone mappings in Banach spaces. Our theorems improve and generalize several results which are announced recently. Our iteration process, method of proof and corollaries are of independent interest