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 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 Endpoints of multi-valued weakly contraction in complete metric spaces endowed with graphs

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4319-4329 ◽  
Author(s):  
Jukrapong Tiammee ◽  
Suthep Suantai
Keyword(s):  
Fixed Point ◽  
Directed Graph ◽  
Metric Space ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered

In this paper, we introduce a new concept of weak G-contraction for multi-valued mappings on a metric space endowed with a directed graph. Endpoint theorem of this mapping is established under some sufficient conditions in a complete metric space endowed with a directed graph. Our main results extend and generalize those fixed point in partially ordered metric spaces. Some examples supporting our main results are also given. Moreover, we apply our main results to obtain some coupled fixed point results in the context of complete metric spaces endowed with a directed graph which are more general than those in partially ordered metric spaces.

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 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 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 Some New Results on Coincidence Points for Multivalued Suzuki-Type Mappings in Fairly Complete Spaces

Computation ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Naeem Saleem ◽  
Iqra Habib ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Coincidence Points ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Contractive Mappings

In this paper, we introduce Suzuki-type ( α , β , γ g ) - generalized and modified proximal contractive mappings. We establish some coincidence and best proximity point results in fairly complete spaces. Also, we provide coincidence and best proximity point results in partially ordered complete metric spaces for Suzuki-type ( α , β , γ g ) - generalized and modified proximal contractive mappings. Furthermore, some examples are presented in each section to elaborate and explain the usability of the obtained results. As an application, we obtain fixed-point results in metric spaces and in partially ordered metric spaces. The results obtained in this article further extend, modify and generalize the various results in the literature.

scholarly journals A Fixed Point Theorem in Orbitally Complete Partially Ordered Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
G. V. R. Babu ◽  
P. D. Sailaja ◽  
K. T. Kidane
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Ordered Set ◽  
Partially Ordered Sets ◽  
Contractive Condition ◽  
Ordered Sets ◽  
Ordered Metric Spaces ◽  
Partially Ordered

Let (X,⪯) be a partially ordered set and T:X→X be a mapping. We prove a fixed point theorem for the map T satisfying a contractive condition in orbits, when X is T-orbitally complete. Our result extends and generalizes the results of Samet et al. (2013) to partially ordered sets. Also, we generalize the results of Ran and Reurings (2004).

scholarly journals Some coincidence point theorems in ordered metric spaces via w-distances

2018 ◽  
Vol 34 (2) ◽  
pp. 207-214
Author(s):  
CHIRASAK MONGKOLKEHA ◽  
◽  
YEOL JE CHO ◽  
◽  
Keyword(s):  
Metric Spaces ◽  
Coincidence Point ◽  
Existence Theorems ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Coincidence Points ◽  
Ordered Metric Spaces ◽  
Partially Ordered

The purpose of this paper is to prove some existence theorems of coincidence points for generalized weak contractions in the setting of partially ordered sets with a metric via w-distances and give some example to illustrate our main results.

scholarly journals Best proximity point results for Suzuki-Edelstein proximal contractions via auxiliary functions

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 435-447 ◽  
Author(s):  
Azhar Hussain ◽  
Muhammad Iqbal ◽  
Nawab Hussain
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Ordered Metric Spaces ◽  
Proximal Contraction ◽  
Contraction Mappings ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Auxiliary Functions

In this paper we study the notion of modified Suzuki-Edelstein proximal contraction under some auxiliary functions for non-self mappings and obtain best proximity point theorems in the setting of complete metric spaces. As applications, we derive best proximity point and fixed point results for such contraction mappings in partially ordered metric spaces. Some examples are given to show the validity of our results. Our results extend and unify many existing results in the literature.

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