Topological developments of \(\mathcal{F}\)-metric spaces

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 di...

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Bibliographic Details
Published in:arXiv.org 2018-06
Main Authors: Bera, Ashis, Dey, Lakshmi Kanta, Garai, Hiranmoy, Chanda, Ankush
Format: Article
Language:English
Subjects:
Fixed points (mathematics)
Metric space
Online Access:Get full text
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Summary: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.
ISSN:2331-8422