scholarly journals On p-Common Best Proximity Point Results for S-Weakly Contraction in Complete Metric Spaces

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 241 ◽  
Author(s):  
Chayut Kongban ◽  
Poom Kumam ◽  
Somayya Komal ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Spaces ◽  
Common Best Proximity Point ◽  
Different Types

In this work, we introduced new notions of a new contraction named S -weakly contraction; after that, we obtained the p-common best proximity point results for different types of contractions in the setting of complete metric spaces by using weak P p -property and proved the uniqueness of these points. Also, we presented some examples to prove the validity of our results.

scholarly journals On p-common Best Proximity Point Results for S-weakly Contraction in Complete Metric Spaces

2018 ◽  
Author(s):  
Chayut Kongban ◽  
Somayya Komal ◽  
Poom Kumam
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Spaces ◽  
Common Best Proximity Point ◽  
Different Types

In this paper, we introduced many new notions and new contraction named as S-weakly contraction after that we obtained the p-common best proximity point theorems for different types of contractions in the setting of complete metric spaces by using weak Pp-property and proved the uniqueness of these points. Also we presented some examples to prove the validity of our results.

scholarly journals Common best proximity points for proximity commuting mapping with Geraghty’s functions

2015 ◽  
Vol 31 (3) ◽  
pp. 359-364
Author(s):  
POOM KUMAM ◽  
◽  
CHIRASAK MONGKOLKEHA ◽  
Keyword(s):  
Recent Result ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Global Minimization ◽  
Objective Functions ◽  
Best Proximity Points ◽  
Complete Metric Spaces ◽  
Multi Objective ◽  
Common Best Proximity Point ◽  
Commuting Mapping

In this paper, we prove new common best proximity point theorems for proximity commuting mapping by using concept of Geraghty’s theorem in complete metric spaces. Our results improve and extend recent result of Sadiq Basha [Basha, S. S., Common best proximity points: global minimization of multi-objective functions, J. Glob Optim, 54 (2012), No. 2, 367-373] and some results in the literature.

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 Results for Generalized Θ-Contractions and Application to Matrix Equations

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 93
Author(s):  
Zhenhua Ma ◽  
Azhar Hussain ◽  
Muhammad Adeel ◽  
Nawab Hussain ◽  
Ekrem Savas
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Positive Definite ◽  
Matrix Equations ◽  
Nonlinear Matrix Equation ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Positive Definite Solution ◽  
Nonlinear Matrix ◽  
Definite Solution

In this paper, we introduce the notion of C ´ iri c ´ type α - ψ - Θ -contraction and prove best proximity point results in the context of complete metric spaces. Moreover, we prove some best proximity point results in partially ordered complete metric spaces through our main results. As a consequence, we obtain some fixed point results for such contraction in complete metric and partially ordered complete metric spaces. Examples are given to illustrate the results obtained. Moreover, we present the existence of a positive definite solution of nonlinear matrix equation X = Q + ∑ i = 1 m A i * γ ( X ) A i and give a numerical example.

scholarly journals A Best Proximity Point Theorem for Generalized Non-Self-Kannan-Type and Chatterjea-Type Mappings and Lipschitzian Mappings in Complete Metric Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Kasamsuk Ungchittrakool
Keyword(s):  
Point Theorem ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Lipschitzian Mappings

The purpose of this paper is to provide and study a best proximity point theorem for generalized non-self-Kannan-type and Chatterjea-type mappings and Lipschitzian mappings in complete metric spaces. The significant mapping in a unified form which related to contractive mappings, Kannan-type mappings, and Chatterjea-type mappings is established. We also provide some examples to illustrate the situation corresponding to the main theorem. The main result of this paper can be viewed as a general and unified form of several previously existing results.

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 Common Best Proximity Point Results for T-GKT Cyclic ϕ-Contraction Mappings in Partial Metric Spaces with Some Applications

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1098
Author(s):  
Nilakshi Goswami ◽  
Raju Roy ◽  
Vishnu Narayan Mishra ◽  
Luis Manuel Sánchez Ruiz
Keyword(s):  
Integral Equation ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Partial Metric ◽  
Existence Of A Solution ◽  
Contraction Mappings ◽  
Common Best Proximity Point ◽  
New Class ◽  
Partial Metric Spaces

The aim of this paper is to derive some common best proximity point results in partial metric spaces defining a new class of symmetric mappings, which is a generalization of cyclic ϕ-contraction mappings. With the help of these symmetric mappings, the characterization of completeness of metric spaces given by Cobzas (2016) is extended here for partial metric spaces. The existence of a solution to the Fredholm integral equation is also obtained here via a fixed-point formulation for such mappings.

scholarly journals Coupled common best proximity point theorems for nonlinear contractions in partially ordered metric spaces

2020 ◽  
Vol 5 (6) ◽  
pp. 6913-6928
Author(s):  
Raju Gopi ◽  
◽  
Veerasamy Pragadeeswarar ◽  
Choonkil Park ◽  
Dong Yun Shin ◽  
...  
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Common Best Proximity Point ◽  
Nonlinear Contractions
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