On a new generalization of metric spaces

TL;DR

This paper introduces the $\\mathcal{F}$-metric space as a broad generalization of metric spaces, explores its topology, and extends the Banach contraction principle within this new framework, supported by illustrative examples.

Contribution

It presents a novel generalization of metric spaces called $\mathcal{F}$-metric spaces and extends fundamental fixed point results to this setting.

Findings

Defined the topology $\tau_{\mathcal{F}}$ for $\mathcal{F}$-metric spaces

Established a new version of the Banach contraction principle in $\mathcal{F}$-metric spaces

Provided multiple examples illustrating the concepts and results

Abstract

In this paper, we introduce the $\mathcal{F}$-metric space concept, which generalizes the metric space notion. We define a natural topology $\tau_{\mathcal{F}}$ in such spaces and we study their topological properties. Moreover, we establish a new version of the Banach contraction principle in the setting of $\mathcal{F}$-metric spaces. Several examples are presented to illustrate our study.