Weak convergence theorems for equilibrium problems and generalized Hybrid mappings

TL;DR

This paper introduces a new iterative method for finding common solutions to equilibrium problems and fixed points of generalized hybrid mappings in Hilbert spaces, extending existing convergence results.

Contribution

The paper proposes a novel modified Ishikawa iteration that generalizes and extends previous methods for equilibrium and hybrid mapping problems.

Findings

Establishes weak convergence of the proposed iteration.

Generalizes existing convergence theorems.

Enriches the theoretical framework for hybrid mappings.

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 generalized hybrid mappings in a Hilbert space. Our results generalize, extend and enrich some existing results in the literature.