Toward a generalized contractive condition in partial metric spaces with the existence results of fixed points and best proximity points

Ninsri, Aphinat; Sintunavarat, Wutiphol

doi:10.1007/s11784-018-0499-4

Cited by 3 publications

(3 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Each partial metric p on a non-empty set X generates a T 0 -topology λ p on X with the family of open p-balls, {B p (x, ) : x ∈ X : > 0}, where B p (x, ) = {y ∈ X : p(x, y) < p(x, x) + }, for all x ∈ X and > 0, as a base of λ p [10,11].…”

Section: Preliminaries and Definitionsmentioning

confidence: 99%

See 1 more Smart Citation

Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

et al. 2021

View full text Add to dashboard Cite

The aim of this paper is to derive some common best proximity point results in partial metric spaces defining a new class of symmetric mappings, which is a generalization of cyclic ϕ-contraction mappings. With the help of these symmetric mappings, the characterization of completeness of metric spaces given by Cobzas (2016) is extended here for partial metric spaces. The existence of a solution to the Fredholm integral equation is also obtained here via a fixed-point formulation for such mappings.

show abstract

Section: Preliminaries and Definitionsmentioning

confidence: 99%

“…In a partial metric space (X, p) the limit of a sequence need not be unique. However, if {x n } and {y n } are sequences in a partial metric space (X, p) such that x n → x and y n → y then p(x n , y n ) need not converge to p(x, y), i.e., p need not be continuous [11].…”

Section: Preliminaries and Definitionsmentioning

confidence: 99%

Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Specifically, different authors have contributed to this topic by obtaining classical metric fixed-point results in the more general context of partial metrics. Such a topic is relevant nowadays (see, for instance, [2][3][4][5][6][7]). Nevertheless, the adaptation of a classical metric, fixed-point result to the partial-metric context does not often actually constitute a generalization but, on the contrary, a particular case.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Partial Metric Spaces and Fixed Point Theorems

et al. 2022

View full text Add to dashboard Cite

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.

show abstract

Existence and Iterative Approximation of Hybrid Best Proximity Points for Set-Valued Mappings^*

Hong

Shao

Luo

2021

Numerical Functional Analysis and Optimization

View full text Add to dashboard Cite

Toward a generalized contractive condition in partial metric spaces with the existence results of fixed points and best proximity points

Cited by 3 publications

References 15 publications

Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

Fuzzy Partial Metric Spaces and Fixed Point Theorems

Existence and Iterative Approximation of Hybrid Best Proximity Points for Set-Valued Mappings^*

Contact Info

Product

Resources

About

Toward a generalized contractive condition in partial metric spaces with the existence results of fixed points and best proximity points

Cited by 3 publications

References 15 publications

Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

Fuzzy Partial Metric Spaces and Fixed Point Theorems

Existence and Iterative Approximation of Hybrid Best Proximity Points for Set-Valued Mappings*

Contact Info

Product

Resources

About

Existence and Iterative Approximation of Hybrid Best Proximity Points for Set-Valued Mappings^*