Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results

[EN] With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see "Am. Math. Month. 1967, 74, 436-437") that a metric space is complete if...

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Bibliographic Details
Authors: Romaguera Bonilla, Salvador|||0000-0001-7857-6139, Tirado Peláez, Pedro
Format: article
Publication Date:2020
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/172295
Online Access:https://riunet.upv.es/handle/10251/172295
Access Level:Open access
Keyword:Fuzzy metric space
Complete
Fixed point
Hicks contraction
MATEMATICA APLICADA
Description
Summary:[EN] With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see "Am. Math. Month. 1967, 74, 436-437") that a metric space is complete if and only if any Banach contraction on any of its closed subsets has a fixed point. We apply our main result to deduce that a well-known fixed point theorem due to D. Mihet (see "Fixed Point Theory 2005, 6, 71-78") also allows us to characterize the fuzzy metric completeness.