Best Proximity Point by Cyclic Geraghty Contraction Map

2015 ◽  
Vol 7 (1) ◽  
pp. 92-96
Author(s):  
Haddadi
Keyword(s):  
Best Proximity Point ◽  
Contraction Map

scholarly journals Existence of fixed point and best proximity point of p-cyclic orbital phi-contraction map

2022 ◽  
Vol 27 (1) ◽  
pp. 91-101
Author(s):  
Prabavathy Magadevan ◽  
Saravanan Karpagam ◽  
Erdal Karapınar
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Best Proximity Point ◽  
Auxiliary Function ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Related Literature ◽  
Contraction Map ◽  
Nonempty Convex ◽  
The Given

In this manuscript, p-cyclic orbital ϕ-contraction map over closed, nonempty, convex subsets of a uniformly convex Banach space X possesses a unique best proximity point if the auxiliary function ϕ is strictly increasing. The given result unifies and extend some existing results in the related literature. We provide an illustrative example to indicate the validity of the observed result.

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]].

A new approach to fractals via best proximity point

2021 ◽  
Vol 146 ◽  
pp. 110850
Author(s):  
Ishak Altun ◽  
Hakan Sahin ◽  
Mustafa Aslantas
Keyword(s):  
Best Proximity Point ◽  
New Approach

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 Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Erdal Karapınar ◽  
V. Pragadeeswarar ◽  
M. Marudai
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Optimal Approximate Solution ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
New Class

We introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.

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