On p-convergent sequences and p-Cauchy sequences in fuzzy metric spaces

Li, Changqing; Zhang, Yan-Lan

doi:10.1016/j.fss.2022.12.020

Cited by 2 publications

(2 citation statements)

References 16 publications

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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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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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“…Then the concept of fuzzy metric spaces was modified by George and Veeramani (1994) . Numerous articles have been published on fuzzy metric spaces (Hussain et al, 2020;Paknazar, 2018;Gregori et al, 2020;Zainab andKider, 2021 Sabri, 2021;Li and Zhang, 2023). F N space was subsequently introduced in different methods by a large number of other mathematicians.…”

Section: Introductionmentioning

confidence: 99%

Best Proximity Point Results in Fuzzy Normed Spaces

Sabri

Ahmed

2023

Sci. Technol. Indones

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Fixed point (briefly FP ) theory is a potent tool for resolving several actual problems since many problems may be simplified to the FP problem. The idea of Banach contraction mapping is a foundational theorem in FP theory. This idea has wide applications in several fields; hence, it has been developed in numerous ways. Nevertheless, all of these results are reliant on the existence and uniqueness of a FP on some suitable space. Because the FP problem could not have a solution in the case of nonself-mappings, the idea of the best proximity point (briefly Bpp) is offered to approach the best solution. This paper investigates the existence and uniqueness of the Bpp of nonself-mappings in fuzzy normed space(briefly FN space) to arrive at the best solution. Following the introduction of the definition of the Bpp, the existence, and uniqueness of the Bpp are shown in a FN space for diverse fuzzy proximal contractions such as ?????? fuzzy proximal contractive mapping and ????h ????h - fuzzy proximal contractive mapping.

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On p-convergent sequences and p-Cauchy sequences in fuzzy metric spaces

Cited by 2 publications

References 16 publications

On Completeness and Fixed Point Theorems in Fuzzy Metric Spaces

On Completeness and Fixed Point Theorems in Fuzzy Metric Spaces

Best Proximity Point Results in Fuzzy Normed Spaces

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