scholarly journals Coupled best proximity point theorem in metric Spaces

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Wutiphol Sintunavarat ◽  
Poom Kumam
Keyword(s):  
Point Theorem ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Coupled Best Proximity Point

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 A Best Proximity Point Theorem for Generalized Non-Self-Kannan-Type and Chatterjea-Type Mappings and Lipschitzian Mappings in Complete Metric Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Kasamsuk Ungchittrakool
Keyword(s):  
Point Theorem ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Lipschitzian Mappings

The purpose of this paper is to provide and study a best proximity point theorem for generalized non-self-Kannan-type and Chatterjea-type mappings and Lipschitzian mappings in complete metric spaces. The significant mapping in a unified form which related to contractive mappings, Kannan-type mappings, and Chatterjea-type mappings is established. We also provide some examples to illustrate the situation corresponding to the main theorem. The main result of this paper can be viewed as a general and unified form of several previously existing results.

scholarly journals Tripled best proximity point theorem in metric spaces

2013 ◽  
pp. 1197-1216 ◽  
Author(s):  
Yeol Je Cho ◽  
Animesh Gupta ◽  
Erdal Karapınar ◽  
Poom Kumam ◽  
Wutiphol Sintunavarat
Keyword(s):  
Point Theorem ◽  
Metric Spaces ◽  
Best Proximity Point

scholarly journals Optimal solutions and applications to nonlinear matrix and integral equations via simulation function

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6087-6106 ◽  
Author(s):  
Azhar Hussain ◽  
Tanzeela Kanwal ◽  
Zoran Mitrovic ◽  
Stojan Radenovic
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Optimal Solutions ◽  
Simulation Function ◽  
Nonlinear Matrix Equation ◽  
Positive Definite Solution ◽  
Nonlinear Matrix ◽  
The Given ◽  
Coupled Best Proximity Point ◽  
Definite Solution

Based on the concepts of ?-proximal admissible mappings and simulation function, we establish some best proximity point and coupled best proximity point results in the context of b-complete b-metric spaces. We also provide some concrete examples to illustrate the obtained results. Moreover, we prove the existence of the solution of nonlinear integral equation and positive definite solution of nonlinear matrix equation X = Q + ?m,i=1 A*i?(X)Ai-?m,i=1 B*i(X)Bi. The given results not only unify but also generalize a number of existing results on the topic in the corresponding literature.

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.

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