Interpolative Metrics Are Not New: A Study of Generalized Contractions in b-Suprametric Spaces

TL;DR

This paper shows that interpolative metrics are a special case of b-metrics and that b-suprametrics generalize b-metrics, extending fixed-point theorems to broader spaces with weaker conditions.

Contribution

It demonstrates the relationships between interpolative metrics, b-metrics, and b-suprametrics, generalizing fixed-point results to these broader spaces.

Findings

Interpolative metrics are a special case of b-metrics.

b-suprametrics generalize b-metrics.

Fixed-point theorems are extended to b-suprametric spaces.

Abstract

{Researchers recently introduced interpolative metric spaces and established fixed-point theorems in this setting. We demonstrate that these metrics are a special case of b-metrics. On the other hand, suprametrics and b-suprametrics have also been introduced, and we show that b-suprametric spaces generalize b-metric spaces. We establish corresponding results previously presented in interpolative metric spaces in the framework of b-suprametric spaces with weaker conditions.