A Picard-S Iterative Scheme for Approximating Fixed Point of Weak-Contraction Mappings

TL;DR

This paper introduces and analyzes a Picard-S iterative scheme for approximating fixed points of weak-contraction mappings, providing convergence and data dependence results to enhance understanding of these iterative methods.

Contribution

The paper presents a new Picard-S iteration method for weak-contraction mappings, including convergence analysis and data dependence results, advancing fixed point approximation techniques.

Findings

Proves convergence of the Picard-S iteration for weak-contraction mappings.

Establishes data dependence results for fixed points.

Provides theoretical foundation for iterative fixed point approximation.

Abstract

We study the convergence analysis of a Picard-S iteration method for a particular class of weak-contraction mappings. Furthermore, we prove a data dependence result for fixed point of the class of weak-contraction mappings with the help of the Picard-S iteration methods.