scholarly journals The existence and uniqueness of $\varphi-$Best proximity point theorems for generalized Boyd-Wong proximal contraction

2020 ◽  
Vol 2020 (-) ◽  
Author(s):  
Urairat Deepan ◽  
Poom Kumam
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Proximal 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 Best proximity point of modified Suzuki-Edelstein-Geraghty type proximal contractions

2020 ◽  
Vol 3 (4) ◽  
pp. 94-104
Author(s):  
Leta Bekere Kumssa ◽  
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Proximal Contraction

In this paper, we introduce the notion of modified Suzuki-Edelstein-Geraghty proximal contraction and prove the existence and uniqueness of best proximity point for such mappings. Our results extend and unify many existing results in the literature. We draw corollaries and give illustrative example to demonstrate the validity of our result.

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.

scholarly journals Best Proximity Results on Dualistic Partial Metric Spaces

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 306 ◽  
Author(s):  
Ariana Pitea
Keyword(s):  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Auxiliary Function ◽  
Partial Metric ◽  
Partial Metric Spaces

We introduce the generalized almost ( φ , θ ) -contractions by means of comparison type functions and another kind of mappings endowed with specific properties in the setting of dualistic partial metric spaces. Also, generalized almost θ -Geraghty contractions in the setting of dualistic partial metric spaces are defined by the use of a function of Geraghty type and another adequate auxiliary function. For these classes of generalized contractions, we have stated and proved the existence and uniqueness of a best proximity point.

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.

scholarly journals Best Proximity Point for Generalized and S -Geraphty Contractions

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Abdelhafid Bassou ◽  
Taoufik Sabar ◽  
Mohamed Aamri
Keyword(s):  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Sufficient Conditions ◽  
New Class

This paper introduces a new class of mappings called S -Geraphty-contractions and provides sufficient conditions for the existence and uniqueness of a best proximity point for such mappings. It also presents the best proximity point result for generalized contractions as well. Our results extend and generalize some theorems in the literature.

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