Convergence of C-Class Enriched Hardy-Rogers Contractions in some Banach Spaces

TL;DR

This paper generalizes enriched Hardy-Rogers contractions using C-class functions in Banach spaces, establishing convergence of fixed points through iterative schemes, thus extending existing fixed point theorems.

Contribution

It introduces a new class of contractions using C-class functions, broadening the scope of fixed point results in Banach spaces.

Findings

Proved convergence of fixed points for the new class of contractions.

Established conditions for the existence of unique and common fixed points.

Generalized recent results in fixed point theory.

Abstract

The applicability of classical Banach contraction mapping principle in solving diverse problems caught the attention of several researchers in various fields of science and engineering. Since its introduction, many extensions and generalizations of this principle continue to emerge in different directions. Some are seen in form of common fixed point using commuting mappings, A-contractions, rational-type contractions, enriched contractions amongst others. In this paper, C-class function is used to generalizing enriched Hargy-Rogers contractions. Convergence of unique fixed point and common fixed points of these general class of mappings were established using some related iterative schemes. Results obtained are generalizations of some recently announced related results in literature.