JAI functional contractions in relational metric spaces

TL;DR

This paper shows that a 2015 fixed point result in relational metric spaces is equivalent to the classical Banach Contraction Principle, unifying several fixed point theorems across different spaces.

Contribution

It establishes the equivalence of a 2015 fixed point theorem in relational metric spaces with the classical Banach Contraction Principle.

Findings

The 2015 fixed point result is equivalent to Banach's contraction principle.

Similar equivalences hold for Edelstein's and Nieto-Rodriguez-Lopez's fixed point results.

Unifies fixed point theorems across various types of metric spaces.

Abstract

The 2015 fixed point result on rs-relational metric spaces due to Alam and Imdad [J. Fixed Point Th. Appl., 17 (2015), 693-702] is equivalent with the classical Banach Contraction Principle [Fund. Math., 3 (1922), 133-181]. This is also valid for the 1961 statement in metric spaces due to Edelstein [Proc. Amer. Math. Soc., 12 (1961), 7-10], or the 2005 fixed point result in quasi-ordered metric spaces obtained by Nieto and Rodriguez-Lopez [Order, 22 (2005), 223-239].