On metric-preserving functions and fixed point theorems

TL;DR

This paper extends fixed point theorems by replacing metric transforms with metric-preserving functions, providing broader conditions and new examples, and analyzing the structure of fixed point sets.

Contribution

It introduces the use of metric-preserving functions in fixed point theorems, generalizing previous results based on metric transforms.

Findings

Extended fixed point theorems using metric-preserving functions

Provided new examples illustrating the theorems

Investigated the structure of fixed point sets

Abstract

Kirk and Shahzad have recently given fixed point theorems concerning local radial contractions and metric transforms. In this article, we replace the metric transforms by metric-preserving functions. This in turn gives several extensions of the main results given by Kirk and Shahzad. Several examples are given. The fixed point sets of metric transforms and metric-preserving functions are also investigated.