scholarly journals Common Best Proximity Point Theorems in JS-Metric Spaces Endowed with Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Chaiporn Thangthong ◽  
Phakdi Charoensawan ◽  
Supreedee Dangskul ◽  
Narawadee Phudolsitthiphat
Keyword(s):  
Binary Relation ◽  
Directed Graph ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Edge Preserving ◽  
Common Best Proximity Point ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

In this paper, we introduce a notion of G -proximal edge preserving and dominating G -proximal Geraghty for a pair of mappings, which will be used to present some existence and uniqueness results for common best proximity points. Here, the mappings are defined on subsets of a JS-metric space endowed with a directed graph. An example is also provided to support the results. Moreover, we apply our result to a similar setting, where the JS-metric space is endowed with a binary relation.

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.

scholarly journals Arbitrary binary relations, contraction mappings and b -metric spaces

2020 ◽  
Vol 72 (4) ◽  
pp. 565-574
Author(s):  
S. Chandok
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Binary Relation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Binary Relations ◽  
Coincidence Points

UDC 517.9We prove some results on the existence and uniqueness of fixed points defined on a b -metric space endowed with an arbitrary binary relation.  As applications, we obtain some statements on coincidence points involving a pair of mappings.  Our results generalize, extend, modify and unify several well-known results especially those obtained by Alam and Imdad [J. Fixed Point Theory and Appl., <strong>17</strong>, 693–702 (2015); Fixed Point Theory, <strong>18</strong>, 415–432 (2017); Filomat, <strong>31</strong>, 4421–4439 (2017)] and Berzig [J. Fixed Point Theory and Appl., <strong>12</strong>, 221–238 (2012)].  Also, we provide an example to illustrate the suitability of results obtained.

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.

scholarly journals Weaker cyclic (phi,phi)-contractive mappings with an application to integro-differential equations

2013 ◽  
Vol 18 (4) ◽  
pp. 427-443 ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Contractive Mapping ◽  
Existence And Uniqueness Results ◽  
Contractive Mappings ◽  
Uniqueness Results ◽  
New Variant ◽  
Cyclic Contractive Mapping

We introduce a new variant of cyclic contractive mapping in a metric space and originate existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. After these results, an application to integro-differential equations is given.

scholarly journals Best Proximity Point Theorems for G , D -Proximal Geraghty Maps in J S -Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Phakdi Charoensawan ◽  
Tanadon Chaobankoh
Keyword(s):  
Binary Relation ◽  
Metric Space ◽  
Metric Spaces ◽  
Best Proximity Point

We study G , D -proximal Geraghty contractions in a J S -metric space X endowed with graph G . We obtain some best proximity theorems for such contractions. An example and several consequences are given. As a consequence of our results, we also provide the best proximity point results in X endowed with a binary relation.

scholarly journals Multi-term fractional differential equations with nonlocal boundary conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 1519-1536
Author(s):  
Bashir Ahmad ◽  
Najla Alghamdi ◽  
Ahmed Alsaedi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
The Given

AbstractWe introduce and study a new kind of nonlocal boundary value problems of multi-term fractional differential equations. The existence and uniqueness results for the given problem are obtained by applying standard fixed point theorems. We also construct some examples for demonstrating the application of the main results.

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