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 and best proximity coupled point in a complete metric space with (P)-property

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 63-74 ◽  
Author(s):  
Wasfi Shatanawi ◽  
Ariana Pitea
Keyword(s):  
Uniqueness Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Comparison Function ◽  
Existence And Uniqueness Theorem

In this paper, we utilize the concept of (P)-property, weak (P)-property and the comparison function to introduce and prove an existence and uniqueness theorem of a best proximity point. Also, we introduce the notion of a best proximity coupled point of a mapping F: X x X ? X. Using this notion and the comparison function to prove an existence and uniqueness theorem of a best proximity coupled point. Our results extend and improve many existing results in the literature. Finally, we introduce examples to support our theorems.

scholarly journals On Fuzzy Contractive Mappings in Fuzzy Metric Spaces

2021 ◽  
Author(s):  
Mohammad Hussein Mohammad Rashid
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Random Operator ◽  
Random Solution ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Contractive Mappings

Abstract In this paper we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in $\tau$-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show that the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.

scholarly journals The Generalized Weaker(α-ϕ-φ)-Contractive Mappings and Related Fixed Point Results in Complete Generalized Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Chi-Ming Chen ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Generalized Metric

We introduce the notion of generalized weaker(α-ϕ-φ)-contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature.

scholarly journals Best Proximity Point Results for Geraghty Type Ƶ-Proximal Contractions with an Application

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 81 ◽  
Author(s):  
Hüseyin Işık ◽  
Hassen Aydi ◽  
Nabil Mlaiki ◽  
Stojan Radenović
Keyword(s):  
Variational Inequality ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Variational Inequality Problem ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Uniqueness Theorems ◽  
Existence And Uniqueness Theorems ◽  
Best Proximity Points ◽  
Inequality Problem

In this study, we establish the existence and uniqueness theorems of the best proximity points for Geraghty type Ƶ-proximal contractions defined on a complete metric space. The presented results improve and generalize some recent results in the literature. An example, as well as an application to a variational inequality problem are also given in order to illustrate the effectiveness of our generalizations.

scholarly journals Best proximity point theorems for proximal multi-valued contractions

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1889-1897
Author(s):  
Nuttawut Bunlue ◽  
Yeol Cho ◽  
Suthep Suantai
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Best Proximity Point ◽  
Nonexpansive Mappings ◽  
Best Proximity Points

In this paper, we introduce new classes of proximal multi-valued contractions in a metric space and proximal multi-valued nonexpansive mappings in a Banach space and show the existence of best proximity points for both classes. Further, for proximal multi-valued nonexpansive mappings, we prove a best proximity point theorem on starshape sets. As a consequence, we also obtain some new fixed point theorems. Finally, we give some examples to illustrate our main results.

scholarly journals A Note on Best Proximity Point Theorems under WeakP-Property

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Angel Almeida ◽  
Erdal Karapınar ◽  
Kishin Sadarangani
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Best Proximity Point ◽  
Late Results ◽  
Point Theory ◽  
Best Proximity Points

In the very recent paper of Akbar and Gabeleh (2013), by using the notion ofP-property, it was proved that some late results about the existence and uniqueness of best proximity points can be obtained from the versions of associated existing results in the fixed point theory. Along the same line, in this paper, we prove that these results can be obtained under a weaker condition, namely, weakP-property.

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 Coincidence Point Results for α , D -Proximal Generalized Geraghty Mappings in J S -Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Atit Wiriyapongsanon ◽  
Phakdi Charoensawan ◽  
Tanadon Chaobankoh
Keyword(s):  
Uniqueness Theorem ◽  
Binary Relation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Existence And Uniqueness Theorem ◽  
Coincidence Points

We introduce a type of Geraghty contractions in a J S -metric space X , called α , D -proximal generalized Geraghty mappings. By using the triangular- α , D -proximal admissible property, we obtain the existence and uniqueness theorem of best proximity coincidence points for these mappings together with some corollaries and illustrative examples. As an application, we give a best proximity coincidence point result in X endowed with a binary relation.

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