Contractive maps in Mustafa-Sims metric spaces

TL;DR

This paper demonstrates that fixed point results in Mustafa-Sims metric spaces can be derived from existing results in standard metric spaces using anticipative contractions, simplifying the understanding of these structures.

Contribution

It shows that fixed point theorems in Mustafa-Sims metric spaces are reducible to classical fixed point results in standard metric spaces.

Findings

Fixed point results in Mustafa-Sims spaces are deducible from standard metric space theorems.

Anticipative contractions serve as a key tool in this reduction.

Simplifies the analysis of Mustafa-Sims metric spaces by linking them to classical metric space theory.

Abstract

The fixed point result in Mustafa-Sims metrical structures obtained by Karapinar and Agarwal [Fixed Point Th. Appl., 2013, 2013:154] is deductible from a corresponding one stated in terms of anticipative contractions over the associated (standard) metric space.