scholarly journals Best Proximity Points for Relatively -Continuous Mappings in Banach and Hyperconvex Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Jack Markin ◽  
Naseer Shahzad
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Best Proximity Points ◽  
Continuous Mappings

We prove some best proximity point results for relatively -continuous mappings in Banach and hyperconvex metric spaces. Our results generalize and extend some recent results to relatively -continuous mappings and to general spaces.

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 Coincidence best proximity points in convex metric spaces

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2451-2463 ◽  
Author(s):  
Moosa Gabeleh ◽  
Olivier Otafudu ◽  
Naseer Shahzad
Keyword(s):  
Integral Equation ◽  
Metric Space ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Best Proximity Points ◽  
Convex Metric Spaces

Let T,S : A U B ? A U B be mappings such that T(A) ? B,T(B)? A and S(A) ? A,S(B)?B. Then the pair (T,S) of mappings defined on A[B is called cyclic-noncyclic pair, where A and B are two nonempty subsets of a metric space (X,d). A coincidence best proximity point p ? A U B for such a pair of mappings (T,S) is a point such that d(Sp,Tp) = dist(A,B). In this paper, we study the existence and convergence of coincidence best proximity points in the setting of convex metric spaces. We also present an application of one of our results to an integral equation.

scholarly journals Random Best Proximity Points for α-Admissible Mappings via Simulation Functions

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 262 ◽  
Author(s):  
Chayut Kongban ◽  
Poom Kumam ◽  
Juan Martínez-Moreno
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Best Proximity Points ◽  
Simulation Functions

In this paper, we introduce a new concept of random α -proximal admissible and random α - Z -contraction. Then we establish random best proximity point theorems for such mapping in complete separable metric spaces.

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.

scholarly journals Common best proximity points for proximity commuting mapping with Geraghty’s functions

2015 ◽  
Vol 31 (3) ◽  
pp. 359-364
Author(s):  
POOM KUMAM ◽  
◽  
CHIRASAK MONGKOLKEHA ◽  
Keyword(s):  
Recent Result ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Global Minimization ◽  
Objective Functions ◽  
Best Proximity Points ◽  
Complete Metric Spaces ◽  
Multi Objective ◽  
Common Best Proximity Point ◽  
Commuting Mapping

In this paper, we prove new common best proximity point theorems for proximity commuting mapping by using concept of Geraghty’s theorem in complete metric spaces. Our results improve and extend recent result of Sadiq Basha [Basha, S. S., Common best proximity points: global minimization of multi-objective functions, J. Glob Optim, 54 (2012), No. 2, 367-373] and some results in the literature.

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 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.

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]].

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