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 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 Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions

2018 ◽  
Vol 19 (1) ◽  
pp. 65
Author(s):  
Md Ahmadullah ◽  
Mohammad Imdad ◽  
Mohammad Arif
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Common Fixed Points ◽  
Common Fixed Point Theorems ◽  
Nonlinear Contractions

In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those are contained in Berzig [J. Fixed Point Theory Appl. 12, 221-238 (2012))]  and Alam and Imdad [To appear in Filomat (arXiv:1603.09159 (2016))]. Interestingly, a corollary to one of our main results under symmetric closure of a binary relation remains a sharpened version of a theorem due to Berzig. Finally, we use examples to highlight the accomplished improvements in the results of this paper.

scholarly journals Relation Theoretic Common Fixed Point Results for Generalized Weak Nonlinear Contractions with an Application

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 49 ◽  
Author(s):  
Atiya Perveen ◽  
Idrees A. Khan ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Binary Relation ◽  
Metric Spaces ◽  
Partial Metric ◽  
System Of Integral Equations ◽  
Partial Metric Spaces ◽  
Nonlinear Contractions

In this paper, by introducing the concept of generalized Ćirić-type weak ( ϕ g , R ) -contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation R . We also deduce some useful consequences showing the usability of our results. Finally, we present an application to establish the solution of a system of integral equations.

scholarly journals Common Fixed Point under Nonlinear Contractions on Quasi Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 453 ◽  
Author(s):  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Nonlinear Contractions

We introduce in this article the notion of ( ψ , ϕ ) - quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence and uniqueness of the fixed point for a couple functions under that contraction.

scholarly journals Coincidence and common fixed point results under generalized (A,S)f-contractions

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2651-2666 ◽  
Author(s):  
Waleed Alfaqih ◽  
Rqeeb Gubran ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Metric Space

Very recently, Shahzad et al. [RACSAM 111 (2017) 307-324] introduced the notion of (A,S)- contractions which unifies several well known nonlinear type contractions (e.g. R-contractions, Z-contractions, L-contractions etc.) in one go. In this paper, we introduce the notion of generalized (A,S)f-contractions and utilize the same to present some coincidence and common fixed point results for a pair of self-mappings (g,f)defined on a metric space endowed with a binary relation S. In this course, we ought to introduce some new notions namely: (I,S)-continuity, (I,S)-compatibility and local (g,f)-transitivity. Consequently, several results involving R-contractions and Z-contractions are deduced. Finally, we furnish illustrative examples to demonstrate the utility of our results.

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.

Coincidence Theorems in New Generalized Metric Spaces Under Locally g-transitive Binary Relation

2018 ◽  
Vol 85 (3-4) ◽  
pp. 396
Author(s):  
Gopi Prasad ◽  
Ramesh Chandra Dimri
Keyword(s):  
Fixed Point ◽  
Binary Relation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Coincidence Theorems ◽  
Transitive Binary Relation

<p>In this paper, we establish coincidence point theorems for contractive mappings, using locally g-transitivity of binary relation in new generalized metric spaces. In the present results, we use some relation theoretic analogues of standard metric notions such as continuity, completeness and regularity. In this way our results extend, modify and generalize some recent fixed point theorems, for instance, Karapinar et al [J. Fixed Point Theory Appl. 18(2016) 645-671], Alam and Imdad [Fixed Point Theory, in press].</p>

scholarly journals On interpolative F-contractions with shrink map

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Monairah Alansari ◽  
Muhammad Usman Ali
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Existence Theorem ◽  
Integral Equations ◽  
Binary Relation ◽  
Metric Space ◽  
Fixed Point Result

AbstractIn this article, we introduce two notions of interpolative F-contractions with shrink map and F-contractions with shrink map. We also study the existence of E-fixed points by using these notations on a metric space endowed with a binary relation. As an application and consequence of the main results, we also get some other interesting results like a common fixed point result, an E-fixed point result on a metric space equipped with graph, and an existence theorem for a solution of integral equations.

scholarly journals Fixed point results for weakly α-admissible pairs

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3697-3713 ◽  
Author(s):  
Ljubomir Ciric ◽  
Vahid Parvaneh ◽  
Nawab Hussain
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Admissible Pair ◽  
Contractive Mappings ◽  
Admissible Pairs

In this paper, we introduce the concepts of weakly and partially weakly ?-admissible pair of mappings and obtain certain coincidence and fixed point theorems for classes of weakly ?-admissible contractive mappings in a b-metric space. As an application, we derive some new coincidence and common fixed point results in a b-metric space endowed with a binary relation or a graph. Moreover, an example is provided here to illustrate the usability of the obtained results.

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