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].

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 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 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 Global optimal approximate solutions of best proximity points

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1555-1564
Author(s):  
Mohammad Haddadi ◽  
Vahid Parvaneh ◽  
Mohammad Mursaleen
Keyword(s):  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
Approximate Solutions ◽  
Point Theory ◽  
Cyclic Contraction ◽  
Best Proximity Points ◽  
Asymptotic Contraction ◽  
Global Optimal ◽  
Necessary And Sufficient

In this paper, we introduce the concept of contractive pair maps and give some necessary and sufficient conditions for existence and uniqueness of best proximity points for such pairs. In our approach, some conditions have been weakened. An application has been presented to demonstrate the usability of our results. Also, we introduce the concept of cyclic ?-contraction and cyclic asymptotic ?-contraction and give some existence and convergence theorems on best proximity point for cyclic ?-contraction and cyclic asymptotic ?-contraction mappings. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory.

scholarly journals BEST PROXIMITY POINT FOR CYCLIC CONTRACTION IN G-METRIC SPACE

2016 ◽  
Vol 12 (2) ◽  
pp. 1-6
Author(s):  
Gopal Meena ◽  
Kanhaiya Jha
Keyword(s):  
Metric Space ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Subject Classification ◽  
Cyclic Contraction ◽  
Cyclic Contraction Mapping

In this paper, we introduce the results of best proximity point in G-metric spaces for the cyclic contraction mapping with an example that illustrates the usability of the obtained results.Mathematics Subject Classification: 41A65, 46B85, 47H25Kathmandu University Journal of Science, Engineering and TechnologyVol. 12, No. 2, 2016, page:1-6

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.

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