Characterizing Complete Fuzzy Metric Spaces Via Fixed Point Results

Salvador Romaguera and Pedro Tirado
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Salvador Romaguera: Instituto Universitario de Matemática Pura y Aplicada-IUMPA, Universitat Politècnica de València, 46022 Valencia, Spain
Pedro Tirado: Instituto Universitario de Matemática Pura y Aplicada-IUMPA, Universitat Politècnica de València, 46022 Valencia, Spain

Mathematics, 2020, vol. 8, issue 2, 1-7

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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