std-Convergence in fuzzy metric spaces

Gregori, Valentı́n; Miñana, Juan-José

doi:10.1016/j.fss.2014.05.007

Cited by 13 publications

(10 citation statements)

References 10 publications

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“…We begin recalling a notion of contractive mapping introduced by Mihet in [15]. It was adapted by Gregori and Miñana in [16] to the George and Veeramani context as follows.…”

Section: Contractivity and Fixed Point Theoremsmentioning

confidence: 99%

Extended Fuzzy Metrics and Fixed Point Theorems

2019

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In this paper, we study those fuzzy metrics M on X, in the George and Veeramani’s sense, such that ⋀ t > 0 M ( x , y , t ) > 0 . The continuous extension M 0 of M to X 2 × 0 , + ∞ is called extended fuzzy metric. We prove that M 0 generates a metrizable topology on X, which can be described in a similar way to a classical metric. M 0 can be used for simplifying or improving questions concerning M; in particular, we expose the interest of this kind of fuzzy metrics to obtain generalizations of fixed point theorems given in fuzzy metric spaces.

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“…We begin recalling a notion of contractive mapping introduced by Mihet in [15]. It was adapted by Gregori and Miñana in [16] to the George and Veeramani context as follows.…”

Section: Contractivity and Fixed Point Theoremsmentioning

confidence: 99%

Extended Fuzzy Metrics and Fixed Point Theorems

2019

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“…Proposition 2 (A. George, P. Veeramani [3]) A sequence {x n } in a fuzzy metric space (X, M, * ) converges to x 0 if and only if lim [13]) Suppose it is given a sequential stronger (weaker, respectively) concept than Cauchy sequence, say s-Cauchy sequence (w-Cauchy, respectively). A concept of convergence, say s-convergence (w-convergence, respectively), is said to be compatible with s-Cauchy (w-Cauchy, respectively), and vice-versa, if the diagram of implications below on the left (on the right, respectively) is fulfilled.…”

Section: Preliminariesmentioning

confidence: 99%

Cauchyness and convergence in fuzzy metric spaces

Gregori

Miñana

Morillas

et al. 2016

RACSAM

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In this paper we survey some concepts of convergence and Cauchyness appeared separately in the context of fuzzy metric spaces in the sense of George and Veeramani. For each convergence (Cauchyness) concept we find a compatible Cauchyness (convergence) concept. We also study the relationship among them and the relationship with compactness and completeness (defined in a natural sense for each one of the Cauchy concepts). In particular, we prove that compactness implies pcompleteness.

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“…Nevertheless, in some cases the natural concepts introduced are non-appropriate. A discussion of this assertion can be found in [4].…”

Section: Introductionmentioning

confidence: 97%

Strong convergence in fuzzy metric spaces

Gregori¹,

Miñana²

2017

Filomat

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In this paper we introduce and study the concept of strong convergence in fuzzy metric spaces (X, M, * ) in the sense of George and Veeramani. This concept is related with the condition t>0 M(x, y, t) > 0, which frequently is required or missing in this context. Among other results we characterize the class of s-fuzzy metrics by the strong convergence defined here and we solve partially the question of finding explicitly a compatible metric with a given fuzzy metric.

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std-Convergence in fuzzy metric spaces

Cited by 13 publications

References 10 publications

Extended Fuzzy Metrics and Fixed Point Theorems

Extended Fuzzy Metrics and Fixed Point Theorems

Cauchyness and convergence in fuzzy metric spaces

Strong convergence in fuzzy metric spaces

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