A parallel hybrid method for equilibrium problems, variational inequalities and nonexpansive mappings in Hilbert space

TL;DR

This paper introduces a new parallel hybrid iterative method to find common solutions for equilibrium problems, variational inequalities, and nonexpansive mappings in Hilbert space, with proven strong convergence.

Contribution

It proposes a novel parallel hybrid iterative scheme with convergence analysis for multiple complex problem classes in Hilbert space.

Findings

Strong convergence of the proposed method is established.

The method effectively handles multiple problem types simultaneously.

A parallel iterative algorithm for combined variational inequalities and nonexpansive mappings is developed.

Abstract

In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone mappings and the set of fixed points of a finite family of nonexpansive mappings in Hilbert space. Strong convergence theorem is proved for the sequence generated by the scheme. Finally, a parallel iterative algorithm for two finite families of variational inequalities and nonexpansive mappings is established.