A Solution of variational inequality problem for a finite family of nonexpansive mappings in Hilbert spaces

TL;DR

This paper introduces an explicit iterative method that converges strongly to a common fixed point of a finite family of nonexpansive mappings in Hilbert spaces, solving the associated variational inequality.

Contribution

It provides a new convergence proof for an explicit iterative process targeting fixed points and variational inequalities in Hilbert spaces.

Findings

Strong convergence of the iterative process is established.

The method effectively finds common fixed points satisfying the variational inequality.

Applicable to finite families of nonexpansive mappings in Hilbert spaces.

Abstract

In this paper we prove the strong convergence of the explicit iterative process to a common fixed point of the finite family of nonexpansive mappings defined on Hilbert space, which solves the the variational inequality on the fixed points set.