Convergence of general composite iterative method for infinite family of nonexpansive mappings in Hilbert spaces

TL;DR

This paper introduces a new composite iterative method using W_n-mapping to find common fixed points of infinite nonexpansive mappings in Hilbert spaces, proving strong convergence and extending previous results.

Contribution

The paper develops a novel composite iterative method for infinite nonexpansive mappings and establishes its strong convergence, improving upon existing methods.

Findings

The iterative method converges strongly to a common fixed point.

The method applies to an infinite family of nonexpansive mappings.

Simulation examples demonstrate the effectiveness of the approach.

Abstract

In this paper by using $W_{n}$-mapping, we introduce a composite iterative method for finding a common fixed point for infinite family of nonexpansive mappings and a solution of a certain variational inequality. Furthermore, the strong convergence of the proposed iterative method is established. Finally, some simulation examples are presented. Our results improve and extend the previous results.