A note on the equivalence of some metric, non-Newtonian and multiplicative metric results

TL;DR

This paper demonstrates that non-Newtonian (including multiplicative) metric spaces are equivalent to standard metric spaces, showing that many fixed point results in non-Newtonian settings can be derived from classical metric space results.

Contribution

It provides a new proof of the equivalence between non-Newtonian and metric spaces, simplifying the understanding of fixed point theorems in these contexts.

Findings

Non-Newtonian metrics are not more general than metric spaces.

Fixed point results in non-Newtonian metrics can be obtained from classical metric results.

The paper offers a different proof of the equivalence between these metric types.

Abstract

In this short note is on the equivalence between non-Newtonian metric (particularly multiplicative metric) and metric. We present a different proof the fact that the notion of a non-Newtonian metric space is not more general than that of a metric space. Also, we emphasize that a lot of fixed point results in the non-Newtonian metric setting can be directly obtained from their metric counterparts.