scholarly journals The Existence and Uniqueness of Coupled Best Proximity Point for Proximally Coupled Contraction in a Complete Ordered Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
V. Pragadeeswarar ◽  
M. Marudai ◽  
P. Kumam ◽  
K. Sitthithakerngkiet
Keyword(s):  
Metric Space ◽  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Ordered Metric Space ◽  
Coupled Best Proximity Point

We prove the existence and uniqueness of coupled best proximity point for mappings satisfying the proximally coupled contraction in a complete ordered metric space. Further, our result provides an extension of a result due to Bhaskar and Lakshmikantham.

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 Best proximity points of contractive mappings on a metric space with a graph and applications

2017 ◽  
Vol 18 (1) ◽  
pp. 13
Author(s):  
Asrifa Sultana ◽  
V. Vetrivel
Keyword(s):  
Fixed Point ◽  
Uniqueness Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Existence And Uniqueness Theorem ◽  
Best Proximity Points ◽  
Contractive Mappings

We establish an existence and uniqueness theorem on best proximity point for contractive mappings on a metric space endowed with a graph. As an application of this theorem, we obtain a result on the existence of unique best proximity point for uniformly locally contractive mappings. Moreover, our theorem subsumes and generalizes many recent  fixed point and best proximity point results.

scholarly journals Best proximity point and best proximity coupled point in a complete metric space with (P)-property

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 63-74 ◽  
Author(s):  
Wasfi Shatanawi ◽  
Ariana Pitea
Keyword(s):  
Uniqueness Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Comparison Function ◽  
Existence And Uniqueness Theorem

In this paper, we utilize the concept of (P)-property, weak (P)-property and the comparison function to introduce and prove an existence and uniqueness theorem of a best proximity point. Also, we introduce the notion of a best proximity coupled point of a mapping F: X x X ? X. Using this notion and the comparison function to prove an existence and uniqueness theorem of a best proximity coupled point. Our results extend and improve many existing results in the literature. Finally, we introduce examples to support our theorems.

scholarly journals Best Proximity Point Results for Geraghty Type Ƶ-Proximal Contractions with an Application

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 81 ◽  
Author(s):  
Hüseyin Işık ◽  
Hassen Aydi ◽  
Nabil Mlaiki ◽  
Stojan Radenović
Keyword(s):  
Variational Inequality ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Variational Inequality Problem ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
Best Proximity Points ◽  
Inequality Problem

In this study, we establish the existence and uniqueness theorems of the best proximity points for Geraghty type Ƶ-proximal contractions defined on a complete metric space. The presented results improve and generalize some recent results in the literature. An example, as well as an application to a variational inequality problem are also given in order to illustrate the effectiveness of our generalizations.

Existence and convergence theorems for best proximity points

2017 ◽  
Vol 11 (01) ◽  
pp. 1850005 ◽  
Author(s):  
M. R. Haddadi
Keyword(s):  
Metric Space ◽  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Multivalued Map ◽  
Convergence Theorems ◽  
Cyclic Contraction ◽  
Best Proximity Points

In this paper, we give new conditions for existence and uniqueness of best proximity point. Also, we introduce the concept of cyclic contraction and nonexpansive for multivalued map and we give existence and convergence theorems for best proximity point in the complete metric space.

scholarly journals Best proximity point theorems for cyclic p-contractions with some consequences and applications

2021 ◽  
Vol 26 (1) ◽  
pp. 113-129
Author(s):  
Mustafa Aslantas ◽  
Hakan Sahin ◽  
Ishak Altun
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Boundary Value ◽  
Uniqueness Result ◽  
Second Order ◽  
Common Solution

In this paper, we introduce the concept of cyclic p-contraction pair for single-valued mappings. Then we present some best proximity point results for such mappings defined on proximally complete pair of subsets of a metric space. Also, we provide some illustrative examples that compared our results with some earliest. Finally, by taking into account a fixed point consequence of our main result we give an existence and uniqueness result for a common solution of a system of second order boundary value problems.

scholarly journals Common Best Proximity Point Theorems in JS-Metric Spaces Endowed with Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Chaiporn Thangthong ◽  
Phakdi Charoensawan ◽  
Supreedee Dangskul ◽  
Narawadee Phudolsitthiphat
Keyword(s):  
Binary Relation ◽  
Directed Graph ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Edge Preserving ◽  
Common Best Proximity Point ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

In this paper, we introduce a notion of G -proximal edge preserving and dominating G -proximal Geraghty for a pair of mappings, which will be used to present some existence and uniqueness results for common best proximity points. Here, the mappings are defined on subsets of a JS-metric space endowed with a directed graph. An example is also provided to support the results. Moreover, we apply our result to a similar setting, where the JS-metric space is endowed with a binary relation.

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.

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