Approximating the common fixed point of enriched interpolative matkowski type mapping in Banach space

TL;DR

This paper introduces a new class of contraction mappings called enriched interpolative Matkowski-type mappings in Banach spaces, aiming to improve fixed point approximation methods for optimization and analysis.

Contribution

It extends existing Matkowski-type contractions with an interpolative enrichment mechanism, providing a novel framework for fixed point analysis in Banach spaces.

Findings

Established existence of fixed points for the new mappings

Demonstrated improved convergence properties

Extended applicability in optimization and numerical analysis

Abstract

In the Normed space theory, the existence of fixed points is one of the main tools in improving efficiency of iterative algorithms in optimization, numerical analysis and various mathematical applications. This study introduces and investigates a recent concept termed "enriched interpolative Matkowski-type mapping". Building upon the well-established foundation of Matkowski-type contractions. This extension incorporates an interpolative enrichment mechanism, yielding a refined framework for analyzing contraction mappings. The proposed concept is motivated by the desire to enhance the convergence behavior and applicability of contraction mapping principles in various mathematical and scientific domains.