Some remarks on the metrizability of $$\mathcal {F}$$-metric spaces

Abstract

In this manuscript, we claim that the newly introduced F-metric space [3, M. Jleli and B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl, 20(3) 2018] is metrizable. Also, we deduce that the notions of convergence, Cauchy sequence, completeness due to Jleli and Samet for F-metric spaces are equivalent with that of usual metric spaces. Moreover, we assert that the Banach contraction principle in the context of F-metric spaces is a direct consequence of its standard metric counterpart.

On a new generalization of metric spaces

“…In our earlier manuscript [4], we have already proved that this new generalization of metric space is indeed metrizable by a metric d : X × X → R defined as follows…”

Some remarks on the metrizability of some well known generalized metric-like structures

“…all. [11] proved that this newly defined structure is metrizable by using the definition of metrizability. However, their proof is technical and a bit lengthy.…”

Boyd-Wong contractions in F-metric spaces and applications

“…However, the general non-linear contractions like Boyd-Wong contraction [8] can't be obtained from the metrizability result. Som et al proved the above facts in [24]. Thus the study of Boyd-Wong fixed point theorem in the context of F-metric spaces seems to be interesting.…”