scholarly journals On Chebyshev centers in metric spaces

2019 ◽  
Vol 106 (120) ◽  
pp. 47-51
Author(s):  
T.D. Narang
Keyword(s):  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Chebyshev Center ◽  
The Subject

A Chebyshev center of a set A in a metric space (X,d) is a point of X best approximating the set A i.e., it is a point x0 ? X such that supy?A d(x0,y) = infx?X supy?A d(x,y). We discuss the existence and uniqueness of such points in metric spaces thereby generalizing and extending several known result on the subject.

Fuzzy double controlled metric spaces and related results

2021 ◽  
Vol 40 (5) ◽  
pp. 9977-9985
Author(s):  
Naeem Saleem ◽  
Hüseyin Işık ◽  
Salman Furqan ◽  
Choonkil Park
Keyword(s):  
Integral Equation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Contraction Principle ◽  
Uniqueness Of Solution ◽  
Contraction Principle ◽  
Triangular Inequality ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M q ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M q ( x , y , t ) ∗ M q ( y , z , s ) . We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.

scholarly journals Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

scholarly journals On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

2021 ◽  
Author(s):  
Mohammad Hussein Mohammad Rashid
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Random Operator ◽  
Random Solution ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Mappings

Abstract In this paper we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in $\tau$-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show that the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

scholarly journals Fixed Point of Almost Contraction in b -Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Maryam Iqbal ◽  
Afshan Batool ◽  
Ozgur Ege ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Almost Contraction ◽  
Specific Mapping

In this paper, we introduce a generalized multivalued ( α , L)-almost contraction in the b -metric space. Furthermore, we prove the existence and uniqueness of the fixed point for a specific mapping. The result presented in this paper extends some of the earlier results in the existing literature. Moreover, some examples are given to illuminate the usability of the obtained results.

scholarly journals Admissible Hybrid Z-Contractions in b-Metric Spaces

Axioms ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 2 ◽  
Author(s):  
Ioan Cristian Chifu ◽  
Erdal Karapınar
Keyword(s):  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Uniqueness Result ◽  
Point Problem ◽  
Well Posedness ◽  
Simulation Functions ◽  
Set Up ◽  
The Given

In this manuscript, we introduce a new notion, admissible hybrid Z -contraction that unifies several nonlinear and linear contractions in the set-up of a b-metric space. In our main theorem, we discuss the existence and uniqueness result of such mappings in the context of complete b-metric space. The given result not only unifies the several existing results in the literature, but also extends and improves them. We express some consequences of our main theorem by using variant examples of simulation functions. As applications, the well-posedness and the Ulam–Hyers stability of the fixed point problem are also studied.

scholarly journals The Generalized Weaker(α-ϕ-φ)-Contractive Mappings and Related Fixed Point Results in Complete Generalized Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Chi-Ming Chen ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of generalized weaker(α-ϕ-φ)-contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature.

scholarly journals Common Fixed Point under Nonlinear Contractions on Quasi Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 453 ◽  
Author(s):  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Nonlinear Contractions

We introduce in this article the notion of ( ψ , ϕ ) - quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence and uniqueness of the fixed point for a couple functions under that contraction.

scholarly journals Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
M. De La Sen ◽  
Asier Ibeas
Keyword(s):  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Points

This paper presents some results concerning the properties of distances and existence and uniqueness of best proximity points ofp-cyclic proximal, weak proximal contractions, and some of their generalizations for the non-self-mappingT:⋃i∈p-Ai→⋃i∈p-Bi  (p≥2), whereAiandBi,∀i∈p-={1,2,…,p}, are nonempty subsets ofXwhich satisfyTAi⊆Bi,∀i∈p-, such that(X,d)is a metric space. The boundedness and the convergence of the sequences of distances in the domains and in their respective image sets of the cyclic proximal and weak cyclic proximal non-self-mapping, and of some of their generalizations are investigated. The existence and uniqueness of the best proximity points and the properties of convergence of the iterates to such points are also addressed.

Fixed point results on complete G-metric spaces

2011 ◽  
Vol 48 (3) ◽  
pp. 304-319 ◽  
Author(s):  
Zead Mustafa ◽  
Mona Khandagji ◽  
Wasfi Shatanawi
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces

In this paper several fixed point theorems for a class of mappings defined on a complete G-metric space are proved. In the same time we show that if the G-metric space (X, G) is symmetric then the existence and uniqueness of these fixed point results follows from the Hardy-Rogers theorem in the induced usual metric space (X, dG). We also prove fixed point results for mapping on a G-metric space (X, G) by using the Hardy-Rogers theorem where (X, G) need not be symmetric.

scholarly journals Complex Valued b-Metric Spaces and Common Fixed Point Theorems under Rational Contractions

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Anil Kumar Dubey
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complex Valued ◽  
Rational Contraction ◽  
Common Fixed Point Theorems

The aim of this paper is to prove the existence and uniqueness of a common fixed point for a pair of mappings satisfying certain rational contraction conditions in complex valued b-metric space. The obtained results generalize and extend some of the well-known results in the literature.

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