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.

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 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].

BEST PROXIMITY POINTS AND FIXED POINTS WITH -FUNCTIONS IN THE FRAMEWORK OF -DISTANCES

2018 ◽  
Vol 99 (03) ◽  
pp. 497-507 ◽  
Author(s):  
ALEKSANDAR KOSTIĆ ◽  
ERDAL KARAPINAR ◽  
VLADIMIR RAKOČEVIĆ
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Spaces ◽  
Best Proximity Points

We study best proximity points in the framework of metric spaces with $w$ -distances. The results extend, generalise and unify several well-known fixed point results in the literature.

scholarly journals On Weak Contractive Cyclic Maps in Generalized Metric Spaces and Some Related Results on Best Proximity Points and Fixed Points

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Nonempty Intersection ◽  
Generalized Metric Spaces ◽  
Best Proximity Points ◽  
Generalized Metric ◽  
Cyclic Maps ◽  
Convergence Of Sequences ◽  
Composite Maps ◽  
Decreasing Functions

This paper discusses the properties of convergence of sequences to limit cycles defined by best proximity points of adjacent subsets for two kinds of weak contractive cyclic maps defined by composite maps built with decreasing functions with either the so-calledr-weaker Meir-Keeler orr,r0-stronger Meir-Keeler functions in generalized metric spaces. Particular results about existence and uniqueness of fixed points are obtained for the case when the sets of the cyclic disposal have a nonempty intersection. Illustrative examples are discussed.

Best Proximity Points and Fixed Points Results for Noncyclic and Cyclic Fisher Quasi-contractions

2019 ◽  
Vol 40 (5) ◽  
pp. 603-619
Author(s):  
Akram Safari-Hafshejani ◽  
Alireza Amini-Harandi ◽  
Majid Fakhar
Keyword(s):  
Fixed Points ◽  
Best Proximity Points

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 Relatively Cyclic and Noncyclic P-Contractions in Locally ?-Convex Space

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 96
Author(s):  
Edraoui Mohamed ◽  
Aamri Mohamed ◽  
Lazaiz Samih
Keyword(s):  
Fixed Points ◽  
Convex Space ◽  
Existence And Uniqueness ◽  
Locally Convex Space ◽  
Best Proximity Points ◽  
Locally Convex ◽  
Convex Spaces

Our main goal of this research is to present the theory of points for relatively cyclic and relatively relatively noncyclic p-contractions in complete locally K -convex spaces by providing basic conditions to ensure the existence and uniqueness of fixed points and best proximity points of the relatively cyclic and relatively noncyclic p-contractions map in locally K -convex spaces. The result of this paper is the extension and generalization of the main results of Kirk and A. Abkar.

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.

scholarly journals Best proximity points of contractive mappings on a metric space with a graph and applications

2017 ◽  
Vol 18 (1) ◽  
pp. 13
Author(s):  
Asrifa Sultana ◽  
V. Vetrivel
Keyword(s):  
Fixed Point ◽  
Uniqueness Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Existence And Uniqueness Theorem ◽  
Best Proximity Points ◽  
Contractive Mappings

We establish an existence and uniqueness theorem on best proximity point for contractive mappings on a metric space endowed with a graph. As an application of this theorem, we obtain a result on the existence of unique best proximity point for uniformly locally contractive mappings. Moreover, our theorem subsumes and generalizes many recent  fixed point and best proximity point results.

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