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 Proximally Compatible Mappings and Common Best Proximity Points

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 353 ◽  
Author(s):  
V. Pragadeeswarar ◽  
R. Gopi ◽  
M. De la Sen ◽  
Stojan Radenović
Keyword(s):  
Best Proximity Point ◽  
Compatible Mappings ◽  
Best Proximity Points ◽  
Common Best Proximity Point

The purpose of this paper is to introduce and analyze a new idea of proximally compatible mappings and we extend some results of Jungck via proximally compatible mappings. Furthermore, we obtain common best proximity point theorems for proximally compatible mappings through two different ways of construction of sequences. In addition, we provide an example to support our main result.

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 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.

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.

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.

scholarly journals Generalized Proximalψ-Contraction Mappings and Best Proximity Points

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Winate Sanhan ◽  
Chirasak Mongkolkeha ◽  
Poom Kumam
Keyword(s):  
Recent Result ◽  
Best Proximity Point ◽  
Best Proximity Points ◽  
Contraction Mappings

We generalized the notion of proximal contractions of the first and the second kinds and established the best proximity point theorems for these classes. Our results improve and extend recent result of Sadiq Basha (2011) and some authors.

scholarly journals Global Optimization and Common Best Proximity Points for Some Multivalued Contractive Pairs of Mappings

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 102 ◽  
Author(s):  
Pradip Debnath ◽  
Hari Mohan Srivastava
Keyword(s):  
Global Optimization ◽  
Best Proximity Point ◽  
Multivalued Mappings ◽  
Best Proximity Points ◽  
Common Best Proximity Point

In this paper, we study a problem of global optimization using common best proximity point of a pair of multivalued mappings. First, we introduce a multivalued Banach-type contractive pair of mappings and establish criteria for the existence of their common best proximity point. Next, we put forward the concept of multivalued Kannan-type contractive pair and also the concept of weak Δ-property to determine the existence of common best proximity point for such a pair of maps.

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].

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