A product topology convergence scheme for finding a function that it's values are common fixed points of a family of representations

TL;DR

This paper introduces a new algorithm in product spaces that converges to a function whose values are common fixed points of a family of nonexpansive mappings, advancing fixed point theory.

Contribution

It presents a novel product topology convergence scheme for finding functions with common fixed points of a family of nonexpansive mappings.

Findings

Algorithm converges in product topology

Identifies common fixed points of nonexpansive mappings

Applicable in Banach space function spaces

Abstract

In this paper, using a family of representations of nonexpansive mappings, we introduce an algorithm in a product space $E^{I}$ consisting of all functions from a nonempty set $I$ to a Banach space $E$. Then we prove the product topology convergence of the proposed algorithm to an element of $E^{I}$ such that it's values are the common fixed points of the representations of the family.