A Characterization of Strong Completeness in Fuzzy Metric Spaces

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

doi:10.3390/math8060861

Cited by 2 publications

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References 27 publications

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“…This fact can also be demonstrated for fuzzy metrics by attending to the results provided in [23]. Since then, many research works have been devoted to the study of both aforementioned concepts of fuzzy metrics (see for instance [4,5,10,9,[12][13][14]24] or recent publications as [11,16,22,28]). Moreover, many results demonstrated to GV -fuzzy metrics can be retrieved for fuzzy metrics, and vice-versa.…”

Section: Introductionmentioning

confidence: 83%

A Banach contraction principle in fuzzy metric spaces defined by means of t-conorms

Gregori

Miñana

2021

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Fixed point theory in fuzzy metric spaces has grown to become an intensive field of research. The difficulty of demonstrating a fixed point theorem in such kind of spaces makes the authors to demand extra conditions on the space other than completeness. In this paper, we introduce a new version of the celebrated Banach contracion principle in the context of fuzzy metric spaces. It is defined by means of t-conorms and constitutes an adaptation to the fuzzy context of the mentioned contracion principle more "faithful" than the ones already defined in the literature. In addition, such a notion allows us to prove a fixed point theorem without requiring any additional condition on the space apart from completeness. Our main result (Theorem 1) generalizes another one proved by Castro-Company and Tirado. Besides, the celebrated Banach fixed point theorem is obtained as a corollary of Theorem 1.

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