Suzuki type unique common fixed point theorem in partial metric spaces using (C)-condition

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.

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Fixed and coincidence point theorems on partial metric spaces with an application

Kumar,

Garakoti,

Chandra

et al. 2023

Mathematica Moravica

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The aim of this paper is to investigate some fixed and co-incidence point theorems in complete, orbitally complete and (T, f)-orbitally complete partial metric spaces under the generalized contractive type conditions of mappings. Moreover, our results generalize and extend the several obtained results in the literature. Additionally some non-trivial examples are demonstrated, and an application has discussed to integral equations.

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Suzuki type unique common fixed point theorem in partial metric spaces using (C)-condition

Abstract: In this paper, we obtain a Suzuki type unique common fixed point theorem using C-condition in partial metric spaces. In addition, we give an example which supports our main theorem.

Cited by 3 publications

References 13 publications

Modified Suzuki-Simulation Type Contractive Mapping in Non-Archimedean Quasi Modular Metric Spaces and Application to Graph Theory

Modified Suzuki-Simulation Type Contractive Mapping in Non-Archimedean Quasi Modular Metric Spaces and Application to Graph Theory

Fuzzy Partial Metric Spaces and Fixed Point Theorems

Fixed and coincidence point theorems on partial metric spaces with an application

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