A New Generalization of Rhoades' Condition

TL;DR

This paper introduces an S-normed space framework to generalize Rhoades' contractive condition, expanding its applicability and providing new theoretical insights with illustrative examples.

Contribution

It proposes a novel generalization of Rhoades' contractive condition within S-normed spaces, extending existing fixed point theory.

Findings

Established a new contractive condition in S-normed spaces

Provided illustrative examples demonstrating the generalization

Extended the scope of fixed point theorems

Abstract

In this paper, our aim is to obtain a new generalization of the well-kown Rhoades' contractive condition. To do this, we introduce the notion of an $S$-normed space. We extend the Rhoades' contractive condition to $S$-normed spaces and define a new type of contractive conditions. We support our theoretical results with necessary illustrative examples.