scholarly journals Best Proximity Point Results for Some Contractive Mappings in Uniform Spaces

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Victoria Olisama ◽  
Johnson Olaleru ◽  
Hudson Akewe
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Uniform Spaces ◽  
Cyclic Contraction ◽  
Proximal Contraction ◽  
Best Proximity Points ◽  
Contractive Mappings ◽  
Proximal Cyclic Contraction

We introduce the concept of Jav-distance (an analogue of b-metric), ϕp-proximal contraction, and ϕp-proximal cyclic contraction for non-self-mappings in Hausdorff uniform spaces. We investigate the existence and uniqueness of best proximity points for these modified contractive mappings. The results obtained extended and generalised some fixed and best proximity points results in literature. Examples are given to validate the main results.

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.

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 Some Random Coupled Best Proximity Points for a Generalized ω-Cyclic Contraction in Polish Spaces

2017 ◽  
Vol 59 (1) ◽  
pp. 91-105 ◽  
Author(s):  
C. Kongban ◽  
P. Kumam
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Cyclic Contraction ◽  
Polish Spaces ◽  
Best Proximity Points ◽  
Coupled Best Proximity Point

AbstractIn this paper, we will introduce the concepts of a random coupled best proximity point and then we prove the existence of random coupled best proximity points in separable metric spaces. Our results extend the previous work of Akbar et al.[1].

scholarly journals Best Proximity Points for Generalizedα-ψ-Proximal Contractive Type Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Points ◽  
New Class ◽  
Contractive Mappings ◽  
Contractive Type

We introduce a new class of non-self-contractive mappings. For such mappings, we study the existence and uniqueness of best proximity points. Several applications and interesting consequences of our obtained results are derived.

scholarly journals A Best Proximity Point Result in Modular Spaces with the Fatou Property

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Mohamed Jleli ◽  
Erdal Karapınar ◽  
Bessem Samet
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
Modular Space ◽  
Fatou Property ◽  
Best Proximity Points ◽  
Modular Spaces

Consider a nonself-mapping , where is a pair of nonempty subsets of a modular space . A best proximity point of is a point satisfying the condition: . In this paper, we introduce the class of proximal quasicontraction nonself-mappings in modular spaces with the Fatou property. For such mappings, we provide sufficient conditions assuring the existence and uniqueness of best proximity points.

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.

scholarly journals Global optimal approximate solutions of best proximity points

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1555-1564
Author(s):  
Mohammad Haddadi ◽  
Vahid Parvaneh ◽  
Mohammad Mursaleen
Keyword(s):  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
Approximate Solutions ◽  
Point Theory ◽  
Cyclic Contraction ◽  
Best Proximity Points ◽  
Asymptotic Contraction ◽  
Global Optimal ◽  
Necessary And Sufficient

In this paper, we introduce the concept of contractive pair maps and give some necessary and sufficient conditions for existence and uniqueness of best proximity points for such pairs. In our approach, some conditions have been weakened. An application has been presented to demonstrate the usability of our results. Also, we introduce the concept of cyclic ?-contraction and cyclic asymptotic ?-contraction and give some existence and convergence theorems on best proximity point for cyclic ?-contraction and cyclic asymptotic ?-contraction mappings. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory.

scholarly journals A Note on Best Proximity Point Theorems under WeakP-Property

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Angel Almeida ◽  
Erdal Karapınar ◽  
Kishin Sadarangani
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Late Results ◽  
Point Theory ◽  
Best Proximity Points

In the very recent paper of Akbar and Gabeleh (2013), by using the notion ofP-property, it was proved that some late results about the existence and uniqueness of best proximity points can be obtained from the versions of associated existing results in the fixed point theory. Along the same line, in this paper, we prove that these results can be obtained under a weaker condition, namely, weakP-property.

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