Some Characterizations of Complete Hausdorff KM-Fuzzy Quasi-Metric Spaces

Salvador Romaguera ()
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Salvador Romaguera: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain

Mathematics, 2023, vol. 11, issue 2, 1-21

Abstract: Gregori and Romaguera introduced, in 2004, the notion of a KM-fuzzy quasi-metric space as a natural asymmetric generalization of the concept of fuzzy metric space in the sense of Kramosil and Michalek. Ever since, various authors have discussed several aspects of such spaces, including their topological and (quasi-)metric properties as well as their connections with domain theory and their relationship with other fuzzy structures. In particular, the development of the fixed point theory for these spaces and other related ones, such as fuzzy partial metric spaces, has received remarkable attention in the last 15 years. Continuing this line of research, we here establish general fixed point theorems for left and right complete Hausdorff KM-fuzzy quasi-metric spaces, which are applied to deduce characterizations of these distinguished kinds of fuzzy quasi-metric completeness. Our approach, which mixes conditions of Suzuki-type with contractions of α − ϕ -type in the well-known proposal of Samet et al., allows us to extend and improve some recent theorems on complete fuzzy metric spaces. The obtained results are accompanied by illustrative and clarifying examples.

Keywords: KM-fuzzy quasi-metric space; left complete; right complete; Suzuki + fuzzy ? ? ? -contractive mapping; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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