A characterization of p-complete fuzzy metric spaces

Gregori, Valentı́n; Miñana, Juan-José; Sala, Bernardino Roig; Sapena, Almanzor

doi:10.1016/j.fss.2021.12.001

Cited by 3 publications

(1 citation statement)

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“…This fact has allowed for the introduction in the literature of some notions in fuzzy metrics that lack sense in the classical context. In this direction, some new notions of convergence, Cauchyness and completeness have been defined in the literature (see [21] and references therein).…”

Section: Introductionmentioning

confidence: 99%

On Completeness and Fixed Point Theorems in Fuzzy Metric Spaces

Gregori,

Miñana,

Roig

et al. 2024

Mathematics

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This paper is devoted to showing the relevance of the notion of completeness used to establish a fixed point theorem in fuzzy metric spaces introduced by Kramosil and Michalek. Specifically, we show that demanding a stronger notion of completeness, called p-completeness, it is possible to relax some extra conditions on the space to obtain a fixed point theorem in this framework. To this end, we focus on a fixed point result, proved by Mihet for complete non-Archimedean fuzzy metric spaces (Theorem 1). So, we define a weaker concept than the non-Archimedean fuzzy metric, called t-strong, and we establish an alternative version of Miheţ’s theorem for p-complete t-strong fuzzy metrics (Theorem 2). In addition, an example of t-strong fuzzy metric spaces that are not non-Archimedean is provided.

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Section: Introductionmentioning

confidence: 99%