A study on the normality of Wijsman topology of a fuzzy metric space

Bashir, Zia; Ullah, Asad

doi:10.1007/s00500-022-07547-1

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2024

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“…Both notions of fuzzy metric spaces have been studied widely from the theoretical point of view and are still being studied today. Indeed, we can find recent references devoted to the study of different topics in this kind of fuzzy metrics such as fixed point theory, convergence and Cauchyness, the Wijsman topology or the asymptotic dimension (see for instance [4][5][6][7][8][9][10][11]).…”

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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