Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results

Romaguera, Salvador; Tirado, Pedro

doi:10.3390/math8020273

Open AccessFeature PaperArticle

Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results

by

Salvador Romaguera

and

Pedro Tirado

^*

Instituto Universitario de Matemática Pura y Aplicada-IUMPA, Universitat Politècnica de València, 46022 Valencia, Spain

^*

Author to whom correspondence should be addressed.

Mathematics 2020, 8(2), 273; https://doi.org/10.3390/math8020273

Submission received: 29 January 2020 / Revised: 11 February 2020 / Accepted: 12 February 2020 / Published: 18 February 2020

(This article belongs to the Special Issue New Advances in Fuzzy Metric Spaces, Soft Metric Spaces, and Other Related Structures)

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Abstract

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.

Keywords: fuzzy metric space; complete; fixed point; hicks contraction

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MDPI and ACS Style

Romaguera, S.; Tirado, P. Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results. Mathematics 2020, 8, 273. https://doi.org/10.3390/math8020273

AMA Style

Romaguera S, Tirado P. Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results. Mathematics. 2020; 8(2):273. https://doi.org/10.3390/math8020273

Chicago/Turabian Style

Romaguera, Salvador, and Pedro Tirado. 2020. "Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results" Mathematics 8, no. 2: 273. https://doi.org/10.3390/math8020273

APA Style

Romaguera, S., & Tirado, P. (2020). Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results. Mathematics, 8(2), 273. https://doi.org/10.3390/math8020273

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results

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