Report
Some remarks on the metrizability of $\mathcal{F}$-metric spaces
| العنوان: | Some remarks on the metrizability of $\mathcal{F}$-metric spaces |
|---|---|
| المؤلفون: | Som, Sumit, Bera, Ashis, Dey, Lakshmi Kanta |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, 54A20, 54E50 |
| الوصف: | In this manuscript, we claim that the newly introduced $\mathcal{F}$-metric space \cite[\, M.~Jleli and B.~Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl, 20(3) 2018]{JS1} is metrizable. Also, we deduce that the notions of convergence, Cauchy sequence, completeness due to Jleli and Samet for $\mathcal{F}$-metric spaces are equivalent with that of usual metric spaces. Moreover, we assert that the Banach contraction principle in the context of $\mathcal{F}$-metric spaces is a direct consequence of its standard metric counterpart. Comment: 10 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1808.02736 |
| رقم الانضمام: | edsarx.1808.02736 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |