Fuzzy Partial Metric Spaces and Fixed Point Theorems

Halis Aygün, Elif Güner, Juan-José Miñana () and Oscar Valero
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Halis Aygün: Department of Mathematics, Faculty of Arts and Science, Kocaeli University, Kocaeli 41380, Turkey
Elif Güner: Department of Mathematics, Faculty of Arts and Science, Kocaeli University, Kocaeli 41380, Turkey
Juan-José Miñana: Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Illes Balears, Spain
Oscar Valero: Departament de Ciències Matemàtiques i Informàtica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Illes Balears, Spain

Mathematics, 2022, vol. 10, issue 17, 1-15

Abstract: Partial metrics constitute a generalization of classical metrics for which self-distance may not be zero. They were introduced by S.G. Matthews in 1994 in order to provide an adequate mathematical framework for the denotational semantics of programming languages. Since then, different works were devoted to obtaining counterparts of metric fixed-point results in the more general context of partial metrics. Nevertheless, in the literature was shown that many of these generalizations are actually obtained as a corollary of their aforementioned classical counterparts. Recently, two fuzzy versions of partial metrics have been introduced in the literature. Such notions may constitute a future framework to extend already established fuzzy metric fixed point results to the partial metric context. The goal of this paper is to retrieve the conclusion drawn in the aforementioned paper by Haghia et al. to the fuzzy partial metric context. To achieve this goal, we construct a fuzzy metric from a fuzzy partial metric. The topology, Cauchy sequences, and completeness associated with this fuzzy metric are studied, and their relationships with the same notions associated to the fuzzy partial metric are provided. Moreover, this fuzzy metric helps us to show that many fixed point results stated in fuzzy metric spaces can be extended directly to the fuzzy partial metric framework. An outstanding difference between our approach and the classical technique introduced by Haghia et al. is shown.

Keywords: fuzzy partial metric; fixed point; completeness; convergence; Cauchyness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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