Characterization of a b-metric space completeness via the existence of a fixed point of Ciric-Suzuki type quasi-contractive multivalued operators and applications

In this article, we present a completeness characterization of b∼metric space via existence of fixed points of generalized multivalued quasicontractions. The purpose of this paper is twofold: (a) to establish the existence of fixed points of multivalued quasicontractions in the setup of b∼ metric spaces and (b) to establish completeness of a b∼ metric space which is a topological property in nature with existence of fixed points of generalized multivalued quasicontractions. Further, a comparison of our results with comparable results shows that the results obtained herein improve and unify the existing results in the literature applicable to the case where existing results fail.

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“…Recently, Alolaiyan et al [27] obtained the following theorem for quasicontractions which is a generalization of results in [7,13,21,25,28,29].…”

Section: Lemma 3 (Seementioning

confidence: 87%

“…Theorem 9. Further, in [27], by considering a class 5 of b ∼ metrics ρ such that for any Cauchy sequence u n and any u in Z, the sequence ρ(u,…”

Section: Lemma 3 (Seementioning

confidence: 99%

Completeness of b∼Metric Spaces and the Fixed Points of Generalized Multivalued Quasicontractions

Ali

Abbas

Sen

2020

Discrete Dynamics in Nature and Society

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“…We give the following theorem. which is a contradiction since h ∈ 0, 1 3 . Hence it should be x = y. Consequently C S x0,r is the unique fixed circle of T .…”

Section: Fixed-circle Theorems Via Auxiliary Functionsmentioning

confidence: 93%

“…Let (X, S) be an S-metric space and C S x0,r be any circle on X. Let us define the mapping for some h ∈ 0, 1 3 and all x, y ∈ X. Then T has a unique fixed point in X.…”

Section: Fixed-circle Theorems Via Auxiliary Functionsmentioning

confidence: 99%

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On the Fixed-Circle Problem

Çelik¹,

Özgür

2021

FU Math Inform

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Presymmetric w-Distances on Metric Spaces

Romaguera,

Tirado

2023

Preprint

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In an outstanding article published in 2008, Suzuki obtained a nice generalization of the Banach contraction principle from which derived a characterization of metric completeness. Although Suzuki’s theorem has been successfully generalized and extended in several directions and contexts, we here show by means of a simple example that the problem of achieving, in an obvious way, its full extension to the framework of w-distances does not have an emphatic response. Motivated by this fact we introduce the concept of presymmetric w-distance on metric spaces, we give some properties and examples of this new structure and show that it provides a reasonable setting to obtain a real and hardly forced w-distance generalization of Suzuki’s theorem. This is realized in our main result, which is a fixed point theorem that involves presymmetric w-distances and certain contractions of Suzuki-type. We also discuss the relationship between our main result and the well-known w-distance full generalization of the Banach contraction principle, due to Suzuki and Takahashi. Connected to this approach we prove another fixed point result that compare with our main result through some examples. Finally, we state a characterization of metric completeness by using our fixed point results.

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Characterization of a b-metric space completeness via the existence of a fixed point of Ciric-Suzuki type quasi-contractive multivalued operators and applications

Cited by 10 publications

References 35 publications

Completeness of b∼Metric Spaces and the Fixed Points of Generalized Multivalued Quasicontractions

Completeness of b∼Metric Spaces and the Fixed Points of Generalized Multivalued Quasicontractions

On the Fixed-Circle Problem

Presymmetric w-Distances on Metric Spaces

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