Correction to: Relation-theoretic metrical fixed-point results via w-distance with applications

Abstract

In this article, utilizing the concept of w-distance, we prove the celebrated Banach's fixed point theorem in metric spaces equipped with an arbitrary binary relation. Necessarily our findings unveil another direction of relation-theoretic metrical fixed point theory. Also, our paper consists of several non-trivial examples which signify the motivation for such investigations. Finally, our obtained results enable us to explore the existence and uniqueness of solutions of nonlinear fractional differential equations involving the Caputo fractional derivative.2010 Mathematics Subject Classification. 47H10, 54H25.

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

“…In this article, by means of the undermentioned Theorem 2.1, we assert that the recently proposed F-metric spaces [3] are metrizable. Hence we also state that the new metric induces same notions of convergence, Cauchy sequence and completeness as that of the usual metric spaces.…”

“…In this section, we deal with the metrizability of newly introduced F-metric spaces defined by Jleli and Samet in [3].…”

“…In [3], the authors presented an examples of F-metric spaces with (f, α) ∈ F × [0, ∞) such that f is continuous in (0, ∞). But here in the subsequent example, we construct an F-metric space with (f, α) ∈ F × [0, ∞) such that f is not continuous at some point in (0, ∞).…”

“…x ∈ X with respect to the metric d which is defined in [3,Theorem 3.1]. (iii) X is F-complete ⇔ X is complete with respect to the metric d which is defined in [3,Theorem 3.1].…”

“…Recently, Jleli and Samet [3] coined another exciting generalization of our usual metric space concept. By means of a certain class of functions, the authors defined the notion of an F-metric space.…”