scholarly journals Relation-theoretic metrical coincidence theorems

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4421-4439 ◽  
Author(s):  
Aftab Alam ◽  
Mohammad Imdad
Keyword(s):  
Binary Relation ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Coincidence Point ◽  
Universal Relation ◽  
Coincidence Points ◽  
Coincidence Theorems

In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, 1-continuity and compatibility to relation-theoretic setting and utilize these relatively weaker notions to prove our results on the existence and uniqueness of coincidence points involving a pair of mappings defined on a metric space endowed with an arbitrary binary relation. Particularly, under universal relation our results deduce the classical coincidence point theorems of Goebel, Jungck and others. Furthermore, our results generalize, modify, unify and extend several well-known results of the existing literature.

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 Relation-theoretic metrical coincidence theorems under weak C-contractions and K-contractions

2021 ◽  
Vol 6 (12) ◽  
pp. 13072-13091
Author(s):  
Faruk Sk ◽  
◽  
Asik Hossain ◽  
Qamrul Haq Khan
Keyword(s):  
Fixed Point ◽  
Binary Relation ◽  
Metric Space ◽  
Coincidence Point ◽  
Auxiliary Function ◽  
Coincidence Theorems ◽  
Transitive Binary Relation

<abstract><p>In this paper, we prove some coincidence point theorems for weak C-contractions and K-contractions involving a new auxiliary function in a metric space endowed with a locally $ f $-transitive binary relation. In this context, we generalize some relevant fixed point results in the literature. Further, we give an example to substantiate the utility of our results.</p></abstract>

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 Partial S-metric spaces and coincidence points

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4613-4626
Author(s):  
Asil Simkhah ◽  
Shaban Sedghi ◽  
Zoran Mitrovic
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Coincidence Points

In this paper, the concept partial S-metric space is introduced as a generalization of S-metric space. We prove certain coincidence point theorems in partial S-metric spaces. The results we obtain generalize many known results in fixed point theory. Also, some examples show the e_ectiveness of this approach.

scholarly journals A NOTE ON PARTIALLY ORDERED FUZZY METRIC SPACE VIA COUPLED COINCIDENCE POINTS

2015 ◽  
Vol 11 (5) ◽  
pp. 5258-5265
Author(s):  
Dr. Arihant Jain ◽  
Vaijayanti Supekar
Keyword(s):  
Metric Space ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Fuzzy Metric Space ◽  
Contractive Condition ◽  
Coincidence Points ◽  
Partially Ordered ◽  
Fuzzy Metric ◽  
Coupled Coincidence Points ◽  
Coupled Coincidence

In this paper, we prove a coupled coincidence point theorem in partially ordered fuzzy metric space using Ï•-contractive condition.

scholarly journals Employing Locally Finitely T-Transitive Binary Relations to Prove Coincidence Theorems for Nonlinear Contractions

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Mohammad Arif ◽  
Idrees A. Khan ◽  
Mohammad Imdad ◽  
Aftab Alam
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Metric Space ◽  
Binary Relations ◽  
Nonlinear Contraction ◽  
Coincidence Theorems ◽  
Nonlinear Contractions ◽  
Transitive Binary Relation

In this article, we prove some relation-theoretic results on coincidence and common fixed point for a nonlinear contraction employing a locally finitely T-transitive binary relation, where T stands for a self-mapping on the underlying metric space. Our newly proved results deduce sharpened versions of certain relevant results of the existing literature. Finally, we adopt some examples to substantiate the genuineness of our proved results herein.

scholarly journals The Study of Fixed Point Theory for Various Multivalued Non-Self-Maps

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Shih Du ◽  
Erdal Karapınar ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Coincidence Points ◽  
Complete Metric Spaces

The basic motivation of this paper is to extend, generalize, and improve several fundamental results on the existence (and uniqueness) of coincidence points and fixed points for well-known maps in the literature such as Kannan type, Chatterjea type, Mizoguchi-Takahashi type, Berinde-Berinde type, Du type, and other types from the class of self-maps to the class of non-self-maps in the framework of the metric fixed point theory. We establish some fixed/coincidence point theorems for multivalued non-self-maps in the context of complete metric spaces.

scholarly journals On Strong Coupled Coincidence Points ofg-Couplings and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Tawseef Rashid ◽  
Qamrul Haq Khan ◽  
Hassen Aydi
Keyword(s):  
Existence And Uniqueness ◽  
Coincidence Point ◽  
Coupled Coincidence Point ◽  
Coincidence Points ◽  
Coupled Coincidence Points ◽  
The Given ◽  
Coupled Coincidence

The purpose of this paper is to prove the existence and uniqueness of a strong coupled coincidence point ofF:X×X→Xandg:X→X, involving Banach and Chatterjea typeg-couplings. We also give some examples and an application in support of the given concepts and our main results.

scholarly journals Probabilistic $ (\omega, \gamma, \phi) $-contractions and coupled coincidence point results

2021 ◽  
Vol 6 (11) ◽  
pp. 11620-11630
Author(s):  
Deepak Jain ◽  
◽  
Manish Jain ◽  
Choonkil Park ◽  
Dong Yun Shin ◽  
...  
Keyword(s):  
Metric Space ◽  
Coincidence Point ◽  
Monotone Operators ◽  
Coupled Coincidence Point ◽  
Fuzzy Metric Space ◽  
Coincidence Points ◽  
Fuzzy Metric ◽  
Coupled Coincidence Points ◽  
Coupled Coincidence ◽  
Mixed Monotone Operators

<abstract><p>In this paper, we introduce the notion of probabilistic $ (\omega, \gamma, \phi) $-contraction and establish the existence coupled coincidence points for mixed monotone operators subjected to the introduced contraction in the framework of ordered Menger $ PM $-spaces with Had${\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over z} }}$ić type $ t $-norm. As an application, a corresponding result in the setup of fuzzy metric space is also obtained.</p></abstract>

scholarly journals Coincidence points in θ - metric spaceS

2021 ◽  
Vol 20 ◽  
pp. 50-55
Author(s):  
Maha Mousa ◽  
Salwa Salman Abed
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Coincidence Points ◽  
Set Valued Mapping

In this paper, inspired by the concept of metric space, two fixed point theorems for α−set-valued mapping T:₳ → CB(₳), h θ (Tp,Tq) ≤ α(dθ(p,q)) dθ(p,q), where α: (0,∞) → (0, 1] such that α(r) < 1, ∀ t ∈ [0,∞) ) are given in complete θ −metric and then extended for two mappings with R-weakly commuting property to obtain a common coincidence point.

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