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arXiv · 1806.05890

Topological developments of $\mathcal{F}$-metric spaces

Ashis Bera·Lakshmi Kanta Dey·Hiranmoy Garai·Ankush Chanda
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Abstract

In this manuscript, we claim that the newly introduced $\mathcal{F}$-metric spaces are Hausdorff and also first countable. Moreover, we assert that every separable $\mathcal{F}$-metric space is second countable. Additionally, we acquire some interesting fixed point results concerning altering distance functions for contractive-type mappings and Kannan-type contractive mappings in this exciting context. However, most of the findings are well-furnished by several non-trivial numerical examples. Finally, we raise an open problem regarding the metrizability of such kind of spaces.

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BibTeXRIS

Ashis Bera, Lakshmi Kanta Dey, Hiranmoy Garai, Ankush Chanda. 2018-06-15. Topological developments of $\mathcal{F}$-metric spaces. https://arxiv.org/abs/1806.05890

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