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.

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 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 Existence of common best proximity point for single and multivalued non-self mappings

2021 ◽  
Vol 37 (2) ◽  
pp. 273-285
Author(s):  
V. PRAGADEESWARAR ◽  
R. GOPI
Keyword(s):  
Coincidence Point ◽  
Best Proximity Point ◽  
Multivalued Mappings ◽  
Sufficient Condition ◽  
Common Best Proximity Point

In this article, we introduce a new concept called proximal E. A property for single and multivalued mappings. We prove existence of proximally coincidence point for such class of mappings. We provide interesting example which illustrates our main results. Finally, we provide sufficient condition for existence of common best proximity point for this class of mappings.

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 Condensing Mappings and Best Proximity Point Results

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Sarah O. Alshehri ◽  
Hamed H. Alsulami ◽  
Naseer Shahzad
Keyword(s):  
Fixed Points ◽  
Best Proximity Point ◽  
Necessary Condition ◽  
Best Proximity Points ◽  
Upper Semicontinuous ◽  
Best Proximity Pair

Best proximity pair results are proved for noncyclic relatively u-continuous condensing mappings. In addition, best proximity points of upper semicontinuous mappings are obtained which are also fixed points of noncyclic relatively u-continuous condensing mappings. It is shown that relative u-continuity of T is a necessary condition that cannot be omitted. Some examples are given to support our results.

scholarly journals CQ-Type Algorithm for Reckoning Best Proximity Points of EP-Operators

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 4 ◽  
Author(s):  
Hassan Houmani ◽  
Teodor Turcanu
Keyword(s):  
Iterative Process ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Convergent Sequence ◽  
Best Proximity Points ◽  
New Class ◽  
Type Algorithm

We introduce a new class of non-self mappings by means of a condition which is called the (EP)-condition. This class includes proximal generalized nonexpansive mappings. It is shown that the existence of best proximity points for (EP)-mappings is equivalent to the existence of an approximate best proximity point sequence generated by a three-step iterative process. We also construct a CQ-type algorithm which generates a strongly convergent sequence to the best proximity point for a given (EP)-mapping.

scholarly journals Existence and Convergence Theorems of Best Proximity Points

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Moosa Gabeleh ◽  
Naseer Shahzad
Keyword(s):  
Banach Spaces ◽  
Convergence Theorem ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Best Proximity Points ◽  
Relatively Nonexpansive Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Relatively Nonexpansive

The aim of this paper is to prove some best proximity point theorems for new classes of cyclic mappings, called pointwise cyclic orbital contractions and asymptotic pointwise cyclic orbital contractions. We also prove a convergence theorem of best proximity point for relatively nonexpansive mappings in uniformly convex Banach spaces.

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