Best proximity point results in dislocated metric spaces via R-functions

2017 ◽  
Vol 112 (4) ◽  
pp. 1391-1407 ◽  
Author(s):  
Leila Gholizadeh ◽  
Erdal Karapınar
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Dislocated Metric ◽  
R Functions

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 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 Fixed Points for a Pair of F-Dominated Contractive Mappings in Rectangular b-Metric Spaces with Graph

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 884 ◽  
Author(s):  
Tahair Rasham ◽  
Giuseppe Marino ◽  
Abdullah Shoaib
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Partial Metric Space ◽  
Contractive Condition ◽  
Partial Metric ◽  
Contractive Mappings ◽  
Dislocated Metric Space ◽  
Definition Of ◽  
Dislocated Metric

Recently, George et al. (in Georgea, R.; Radenovicb, S.; Reshmac, K.P.; Shuklad, S. Rectangular b-metric space and contraction principles. J. Nonlinear Sci. Appl. 2015, 8, 1005–1013) furnished the notion of rectangular b-metric pace (RBMS) by taking the place of the binary sum of triangular inequality in the definition of a b-metric space ternary sum and proved some results for Banach and Kannan contractions in such space. In this paper, we achieved fixed-point results for a pair of F-dominated mappings fulfilling a generalized rational F-dominated contractive condition in the better framework of complete rectangular b-metric spaces complete rectangular b-metric spaces. Some new fixed-point results with graphic contractions for a pair of graph-dominated mappings on rectangular b-metric space have been obtained. Some examples are given to illustrate our conclusions. New results in ordered spaces, partial b-metric space, dislocated metric space, dislocated b-metric space, partial metric space, b-metric space, rectangular metric spaces, and metric space can be obtained as corollaries of our results.

Best proximity point theorems in b-metric spaces

2018 ◽  
Vol 27 (3) ◽  
pp. 859-866
Author(s):  
J. Maria Joseph ◽  
J. Beny ◽  
M. Marudai
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point

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 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 point results in geodesic metric spaces

2012 ◽  
Vol 2012 (1) ◽  
pp. 234 ◽  
Author(s):  
Maryam A Alghamdi ◽  
Mohammed A Alghamdi ◽  
Naseer Shahzad
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Geodesic Metric
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