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arXiv · 1803.00240

On a new generalization of metric spaces

Mohamed Jleli·Bessem Samet
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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.

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Mohamed Jleli, Bessem Samet. 2018-03-01. On a new generalization of metric spaces. https://arxiv.org/abs/1803.00240

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