On the g-best proximity point results for G-generalized proximal contraction mappings in G-metric spaces

2015 ◽  
Author(s):  
Aynur Şahin ◽  
Metin Başarır ◽  
Safeer Hussain Khan
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Proximal Contraction ◽  
Contraction Mappings ◽  
Generalized Proximal Contraction

scholarly journals Best proximity point results for Suzuki-Edelstein proximal contractions via auxiliary functions

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 435-447 ◽  
Author(s):  
Azhar Hussain ◽  
Muhammad Iqbal ◽  
Nawab Hussain
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Ordered Metric Spaces ◽  
Proximal Contraction ◽  
Contraction Mappings ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Auxiliary Functions

In this paper we study the notion of modified Suzuki-Edelstein proximal contraction under some auxiliary functions for non-self mappings and obtain best proximity point theorems in the setting of complete metric spaces. As applications, we derive best proximity point and fixed point results for such contraction mappings in partially ordered metric spaces. Some examples are given to show the validity of our results. Our results extend and unify many existing results in the literature.

scholarly journals The Existence Theorems of an Optimal Approximate Solution for Generalized Proximal Contraction Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Wutiphol Sintunavarat ◽  
Poom Kumam
Keyword(s):  
Approximate Solution ◽  
Best Proximity Point ◽  
Existence Theorems ◽  
Contraction Principle ◽  
Optimal Approximate Solution ◽  
Proximal Contraction ◽  
Contraction Mappings ◽  
Generalized Proximal Contraction ◽  
Banach’S Contraction Principle

Recently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contractions of the first and second kinds which are more general than the notion of self-contractions, establish the existence of an optimal approximate solution theorems for these non-self-mappings, and also give examples to validate our main results.

scholarly journals Best Proximity Point Results inG-Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
N. Hussain ◽  
A. Latif ◽  
P. Salimi
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Point Theory ◽  
Rich Source ◽  
Point Problem ◽  
Proximal Contraction ◽  
Contraction Mappings

G-metric spaces proved to be a rich source for fixed point theory; however, the best proximity point problem has not been considered in such spaces. The aim of this paper is to introduce certain new classes of proximal contraction mappings and establish the best proximity point theorems for such kind of mappings inG-metric spaces. As a consequence of these results, we deduce certain new best proximity and fixed point results. Moreover, we present an example to illustrate the usability of the obtained results.

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 Existence of Best Proximity Point with an Application to Nonlinear Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Shagun Sharma ◽  
Sumit Chandok
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Contraction Mappings

Using the idea of modified ϱ -proximal admissible mappings, we derive some new best proximity point results for ϱ − ϑ -contraction mappings in metric spaces. We also provide some illustrations to back up our work. As a result of our findings, several fixed-point results for such mappings are also found. We obtain the existence of a solution for nonlinear integral equations as an application.

scholarly journals Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1098
Author(s):  
Nilakshi Goswami ◽  
Raju Roy ◽  
Vishnu Narayan Mishra ◽  
Luis Manuel Sánchez Ruiz
Keyword(s):  
Integral Equation ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Partial Metric ◽  
Existence Of A Solution ◽  
Contraction Mappings ◽  
Common Best Proximity Point ◽  
New Class ◽  
Partial Metric Spaces

The aim of this paper is to derive some common best proximity point results in partial metric spaces defining a new class of symmetric mappings, which is a generalization of cyclic ϕ-contraction mappings. With the help of these symmetric mappings, the characterization of completeness of metric spaces given by Cobzas (2016) is extended here for partial metric spaces. The existence of a solution to the Fredholm integral equation is also obtained here via a fixed-point formulation for such mappings.

scholarly journals A Discussion on the Existence of Best Proximity Points That Belong to the Zero Set

Axioms ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 19 ◽  
Author(s):  
Erdal Karapınar ◽  
Mujahid Abbas ◽  
Sadia Farooq
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Zero Set ◽  
Related Literature ◽  
Proximal Contraction ◽  
Best Proximity Points

In this paper, we investigate the existence of best proximity points that belong to the zero set for the α p -admissible weak ( F , φ ) -proximal contraction in the setting of M-metric spaces. For this purpose, we establish φ -best proximity point results for such mappings in the setting of a complete M-metric space. Some examples are also presented to support the concepts and results proved herein. Our results extend, improve and generalize several comparable results on the topic in the related literature.

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