New Fixed Point Results in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="bold-script">F</mml:mi></mml:math>-Quasi-Metric Spaces and an Application

Ghasab, Ehsan Lotfali; Majani, Hamid; Karapınar, Erdal; Rad, Ghasem Soleimani

doi:10.1155/2020/9452350

Cited by 8 publications

(4 citation statements)

References 10 publications

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“…Besides this, one can strive to obtain weaker conditions to ensure the existence of the best proximity points for some generalized proximal contractions in several classical metric spaces; for instance, the existence of a proximity point without P−property in a fuzzy metric space would be worth investigating. Moreover, Ghasab et al [35] introduced F −quasi-metric spaces, which is viewed as a generalization of F −metric spaces. One could extend our main results to the F −quasi-metric spaces for furnishing the best proximity theory.…”

Section: Discussionmentioning

confidence: 99%

Common Best Proximity Points and Completeness of ℱ−Metric Spaces

et al. 2023

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In this paper, we introduce three classes of proximal contractions that are called the proximally λ−ψ−dominated contractions, generalized ηβγ−proximal contractions and Berinde-type weak proximal contractions, and obtain common best proximity points for these proximal contractions in the setting of F−metric spaces. Further, we obtain the best proximity point result for generalized α−φ−proximal contractions in F−metric spaces. As an application, fixed point and coincidence point results for these contractions are obtained. Some examples are provided to support the validity of our main results. Moreover, we obtain a completeness characterization of the F−metric spaces via best proximity points.

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Section: Discussionmentioning

confidence: 99%

Common Best Proximity Points and Completeness of ℱ−Metric Spaces

et al. 2023

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“…Romaguera [6] discussed fixed point results for generalized Ćirić's contractions of quasi-metric spaces. Ghasab et al [7] presented some new fixed point results in F -quasi-metric spaces and an application.…”

Section: Introductionmentioning

confidence: 99%

Existence of Fixed Points of Suzuki-Type Contractions of Quasi-Metric Spaces

Ali,

Nazir

et al. 2023

Mathematics

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In order to generalize classical Banach contraction principle in the setup of quasi-metric spaces, we introduce Suzuki-type contractions of quasi-metric spaces and prove some fixed point results. Further, we suggest a correction in the definition of another class of quasi-metrics known as Δ-symmetric quasi-metrics satisfying a weighted symmetry property. We discuss equivalence of various types of completeness of Δ-symmetric quasi-metric spaces. At the end, we consider the existence of fixed points of generalized Suzuki-type contractions of Δ-symmetric quasi-metric spaces. Some examples have been furnished to make sure that generalizations we obtain are the proper ones.

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“…Partly stimulated by these developments, the research about the fixed point theory on quasi-metric spaces has received a powerful boost in the last 12 years, during which many papers have been published in this area, so we will limit ourselves here to citing some of the most recent ones [15][16][17][18][19][20][21][22] with the references therein.…”

Section: Introductionmentioning

confidence: 99%

Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results

Romaguera

2022

Mathematics

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This paper deals with the question of achieving a suitable extension of the notion of Suzuki-type contraction to the framework of quasi-metric spaces, which allows us to obtain reasonable fixed point theorems in the quasi-metric context. This question has no an easy answer; in fact, we here present an example of a self map of Smyth complete quasi-metric space (a very strong kind of quasi-metric completeness) that fulfills a simple and natural contraction of Suzuki-type but does not have fixed points. Despite it, we implement an approach to obtain two fixed point results, whose validity is supported with several examples. Finally, we present a general method to construct non-T1 quasi-metric spaces in such a way that it is possible to systematically generate non-Banach contractions which are of Suzuki-type. Thus, we can apply our results to deduce the existence and uniqueness of solution for some kinds of functional equations which is exemplified with a distinguished case.

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New Fixed Point Results in F-Quasi-Metric Spaces and an Application

Cited by 8 publications

References 10 publications

Common Best Proximity Points and Completeness of ℱ−Metric Spaces

Common Best Proximity Points and Completeness of ℱ−Metric Spaces

Existence of Fixed Points of Suzuki-Type Contractions of Quasi-Metric Spaces

Basic Contractions of Suzuki-Type on Quasi-Metric Spaces and Fixed Point Results

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