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 point theorems for G-proximal weak contractions in complete metric spaces endowed with graphs

2018 ◽  
Vol 34 (1) ◽  
pp. 65-75
Author(s):  
CHALONGCHAI KLANARONG ◽  
◽  
SUTHEP SUANTAI ◽  
Keyword(s):  
Directed Graph ◽  
Metric Space ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Special Case

In this paper, the existence of best proximity point theorems for two new types of nonlinear non-self mappings in a complete metric space endowed with a directed graph are established. Our main results extend and generalize many known results in the literatures. As a special case of the main results, the best proximity point theorems on partially ordered sets are obtained.

On a theorem of Brian Fisher in the framework of w-distance

2017 ◽  
Vol 33 (2) ◽  
pp. 199-205
Author(s):  
DARKO KOCEV ◽  
◽  
VLADIMIR RAKOCEVIC ◽  
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
Common Fixed Points ◽  
Complete Metric Spaces ◽  
Condition C ◽  
Relaxing Condition

In 1980. Fisher in [Fisher, B., Results on common fixed points on complete metric spaces, Glasgow Math. J., 21 (1980), 165–167] proved very interesting fixed point result for the pair of maps. In 1996. Kada, Suzuki and Takahashi introduced and studied the concept of w–distance in fixed point theory. In this paper, we generalize Fisher’s result for pair of mappings on metric space to complete metric space with w–distance. The obtained results do not require the continuity of maps, but more relaxing condition (C; k). As a corollary we obtain a result of Chatterjea.

scholarly journals Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kushal Roy ◽  
Sayantan Panja ◽  
Mantu Saha ◽  
Zoran D. Mitrović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Weak Contraction ◽  
Complete Metric Spaces ◽  
Contractive Mappings

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, Ćirić-quasi contraction and weak contraction in the framework of a metric space. We prove some fixed point theorems for such type of mappings over complete metric spaces with the help of φ-diminishing property. Some examples are given in strengthening the hypothesis of our established theorems.

scholarly journals Approximation fixed theorems for α-partial weakly Zamfirescu mappings with application to homotopy invariance

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1941-1956
Author(s):  
Aphinat Ninsri ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Binary Relation ◽  
Metric Space ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Homotopy Invariance ◽  
Complete Metric Spaces ◽  
Approximate Fixed Point

In this paper, we introduce the concept of ?-partial weakly Zamfirescu mappings and give some approximate fixed point results for this mapping in ?-complete metric spaces. We also give some approximate fixed point results in ?-complete metric space endowed with an arbitrary binary relation and approximate fixed point results in ?-complete metric space endowed with graph. As application, we give homotopy results for ?-partial weakly Zamfirescu mapping.

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 Tripled best proximity point in complete metric spaces

2020 ◽  
Vol 18 (1) ◽  
pp. 204-210 ◽  
Author(s):  
Yumnam Rohen ◽  
Nabil Mlaiki
Keyword(s):  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Spaces ◽  
New Type

Abstract In this paper, we introduce a new type of contraction to seek the existence of tripled best proximity point results. Here, using the new contraction and P-property, we generalize and extend results of W. Shatanawi and A. Pitea and prove the existence and uniqueness of some tripled best proximity point results. Examples are also given to support our results.

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 A Best Proximity Point Theorem for G-Proximal (delta, 1-delta) Weak Contraction in Complete Metric Space Endowed with a Graph

2019 ◽  
pp. 91-96
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Point Theorem ◽  
Metric Space ◽  
Best Proximity Point ◽  
Complete Metric Space ◽  
Weak Contraction

The notion of (delta, 1-delta) weak contraction appeared in [1]. In this paper, we consider that the map satisfying the (delta, 1-delta) weak contraction is a non-self map, and obtain a best proximity point theorem in complete metric space endowed with a graph.

scholarly journals Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 327 ◽  
Author(s):  
Naeem Saleem ◽  
Mujahid Abbas ◽  
Manuel Sen
Keyword(s):  
Approximate Solution ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fuzzy Metric Space ◽  
Optimal Approximate Solution ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric

The purpose of this paper is to introduce α f -proximal H -contraction of the first and second kind in the setup of complete fuzzy metric space and to obtain optimal coincidence point results. The obtained results unify, extend and generalize various comparable results in the literature. We also present some examples to support the results obtained herein.

scholarly journals Two Fixed Point Theorems Concerning F-Contraction in Complete Metric Spaces

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 58 ◽  
Author(s):  
Ovidiu Popescu ◽  
Gabriel Stan
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Complete Metric Space ◽  
Point Theory ◽  
The Self ◽  
Complete Metric Spaces

In this paper, we generalize some results of Wardowski (Fixed Point Theory Appl. 2012:94, 2012), Cosentino and Vetro (Filomat 28:4, 2014), and Piri and Kumam (Fixed Point Theory Appl. 2014:210, 2014) theories by applying some weaker symmetrical conditions on the self map of a complete metric space and on the mapping F, concerning the contractions defined by Wardowski.

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