Alternative iterative methods for nonexpansive mappings, rates of convergence and application

TL;DR

This paper introduces new iterative methods for nonexpansive mappings in Banach spaces, proving their convergence to solutions of fixed point and variational inequality problems, with established convergence rates and practical applications.

Contribution

It proposes alternative iterative algorithms with proven convergence and rates for nonexpansive mappings, expanding the toolkit for fixed point and variational inequality problems.

Findings

Convergent iterative methods for nonexpansive mappings are developed.

Rates of asymptotic regularity are established using proof-theoretic techniques.

Applications demonstrating the effectiveness of the methods are provided.

Abstract

Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such iterations using proof-theoretic techniques. Some applications of the convergence results are presented.