scholarly journals Best proximity point theorems for probabilistic proximal cyclic contraction with applications in nonlinear programming

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Reza Saadati
Keyword(s):  
Nonlinear Programming ◽  
Best Proximity Point ◽  
Cyclic Contraction ◽  
Proximal Cyclic Contraction

scholarly journals Best Proximity Point Results for Some Contractive Mappings in Uniform Spaces

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Victoria Olisama ◽  
Johnson Olaleru ◽  
Hudson Akewe
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Uniform Spaces ◽  
Cyclic Contraction ◽  
Proximal Contraction ◽  
Best Proximity Points ◽  
Contractive Mappings ◽  
Proximal Cyclic Contraction

We introduce the concept of Jav-distance (an analogue of b-metric), ϕp-proximal contraction, and ϕp-proximal cyclic contraction for non-self-mappings in Hausdorff uniform spaces. We investigate the existence and uniqueness of best proximity points for these modified contractive mappings. The results obtained extended and generalised some fixed and best proximity points results in literature. Examples are given to validate the main results.

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 Theorems for a Berinde MT-Cyclic Contraction on a Semisharp Proximal Pair

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Chalongchai Klanarong ◽  
Tanadon Chaobankoh
Keyword(s):  
Metric Space ◽  
Best Proximity Point ◽  
Cyclic Contraction ◽  
Cyclic Contractions ◽  
New Type

In this paper, a new type of non-self-mapping, called Berinde MT-cyclic contractions, is introduced and studied. Best proximity point theorems for this type of mappings in a metric space are presented. Some examples illustrating our main results are also given. Our results generalize and improve some known results in the literature.

scholarly journals Best Proximity Point Theorems for Two Weak Cyclic Contractions on Metric-Like Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 349 ◽  
Author(s):  
Erdal Karapınar ◽  
Chi-Ming Chen ◽  
Chih-Te Lee
Keyword(s):  
Recent Literature ◽  
Best Proximity Point ◽  
Cyclic Contraction ◽  
Cyclic Contractions

In this paper, we establish two best proximity point theorems in the setting of metric-like spaces that are based on cyclic contraction: Meir–Keeler–Kannan type cyclic contractions and a generalized Ćirić type cyclic φ -contraction via the MT -function. We express some examples to indicate the validity of the presented results. Our results unify and generalize a number of best proximity point results on the topic in the corresponding recent literature.

scholarly journals Best Proximity Points for Some Classes of Proximal Contractions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Naseer Shahzad ◽  
Francesca Vetro
Keyword(s):  
Approximate Solution ◽  
Nonlinear Programming ◽  
Programming Problem ◽  
Iterative Algorithm ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
Nonlinear Programming Problem ◽  
Optimal Approximate Solution ◽  
Unique Point ◽  
Banach’S Contraction Principle

Given a self-mapping and a non-self-mapping , the aim of this work is to provide sufficient conditions for the existence of a unique point , calledg-best proximity point, which satisfies . In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function , thereby getting an optimal approximate solution to the equation . An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-self-mappings.

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.

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