scholarly journals Existence and Uniqueness of Best Proximity Points for Generalized Almost Contractions

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Chirasak Mongkolkeha ◽  
Chayut Kongban ◽  
Poom Kumam
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Almost Contraction ◽  
Best Proximity Points ◽  
Contraction Mappings

The purpose of this paper is to elicit some interesting extensions of generalized almost contraction mappings to the case of non-self-mappings withα-proximal admissible and prove best proximity point theorems for this classes. Moreover, we also give some examples and applications to support our main results.

C-class functions and pair (F,h) Upper class on common best proximity points results for new proximal C-contraction mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3459-3471
Author(s):  
A.H. Ansari ◽  
Geno Jacob ◽  
D. Chellapillai
Keyword(s):  
Best Proximity Point ◽  
Upper Class ◽  
Best Proximity Points ◽  
Contraction Mappings ◽  
Common Best Proximity Point

In this paper, using the concept of C-class and Upper class functions we prove the existence of unique common best proximity point. Our main result generalizes results of Kumam et al. [[17]] and Parvaneh et al. [[21]].

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 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 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.

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 for Generalized Proximal Weak Contractions Satisfying Rational Expression on Ordered Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Weak Contraction ◽  
Ordered Metric Spaces ◽  
Best Proximity Points ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Rational Expression ◽  
Rational Type

We introduce a generalized proximal weak contraction of rational type for the non-self-map and proved results to ensure the existence and uniqueness of best proximity point for such mappings in the setting of partially ordered metric spaces. Further, our results provides an extension of a result due to Luong and Thuan (2011) and also it provides an extension of Harjani (2010) to the case of self-mappings.

Existence of best proximity points satisfying two constraint inequalities

2021 ◽  
pp. 2250104
Author(s):  
D. Balraj ◽  
J. Geno Kadwin ◽  
M. Marudai
Keyword(s):  
Partial Order ◽  
Critical Points ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Proximal Contraction ◽  
Best Proximity Points ◽  
Contraction Mappings ◽  
Constraint Inequalities ◽  
Coupled Best Proximity Point

In this paper, we prove the existence of best proximity point and coupled best proximity point on metric spaces with partial order for weak proximal contraction mappings such that these critical points satisfy some constraint inequalities.

scholarly journals Best Proximity point for Z-contraction and Suzuki type Z-contraction mappings with an application to fractional calculus

2016 ◽  
Vol 17 (2) ◽  
pp. 185 ◽  
Author(s):  
Somayya Komal ◽  
Poom Kumam ◽  
Dhananjay Gopal
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Contraction Mappings ◽  
Complete Metric Spaces ◽  
Functional Differential

In this article, we introduced the best proximity point theorems for $\mathcal{Z}$-contraction and Suzuki type $\mathcal{Z}$-contraction in the setting of complete metric spaces. Also by the help of weak $P$-property and $P$-property, we proved existence and uniqueness of best proximity point. There is a simple example to show the validity of our results. Our results extended and unify many existing results in the literature. Moreover, an application to fractional order functional differential equation is discussed.<br /><br />

scholarly journals Generalized 2-proximal C-contraction mappings in complete ordered 2-metric space and their best proximity points

2020 ◽  
Vol 12 (1) ◽  
pp. 1-11 ◽  
Author(s):  
A.G. Sanatee ◽  
M. Iranmanesh ◽  
L.N. Mishra ◽  
V.N. Mishra
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Best Proximity Points ◽  
Contraction Mappings ◽  
Contraction Type

In this paper, we extend the concept of best proximity point to 2-metric spaces and prove the existence of such points for contraction type non-self mappings in the setting of complete 2-metric spaces. Also, we presented an example to support our results.

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