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 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 Fixed point theorems for nonlinear contractive mappings in ordered b-metric space with auxiliary function

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Namana Seshagiri Rao ◽  
Karusala Kalyani ◽  
Belay Mitiku
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Auxiliary Function ◽  
Weak Contraction ◽  
Partially Ordered ◽  
Contractive Mappings ◽  
Contraction Condition

Abstract Objectives In this paper we present some fixed point theorems for self mappings satisfying generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction condition in partially ordered complete b-metric spaces. The results presented over here generalize and extend some existing results in the literature. Finally, we illustrate two examples to support our results. Result We obtained a unique fixed point of a self mapping satisfying certain contraction condition which is involving an auxiliary function. Also, the results are presented for the existence of a common fixed point and a coincidence point for generalized $$(\phi , \psi )$$ ( ϕ , ψ ) -weak contraction mappings in partially ordered complete b-metric space.

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 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 The Existence of Fixed Point Theorems via -Distance and -Admissible Mappings and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Marwan Amin Kutbi ◽  
Wutiphol Sintunavarat
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Binary Relation ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Generalized Contraction ◽  
Common Fixed Point Theorems

We introduce the concept of the generalized -contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of -distance and -admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature.

scholarly journals Coincidence Point Results on Relation Theoretic F w , R g -Contractions and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Muhammad Aslam ◽  
Hassen Aydi ◽  
Samina Batul ◽  
Amna Naz
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Additional Condition ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Ordered Metric Spaces ◽  
Weakly Compatible ◽  
Type Integral ◽  
Common Fixed Point Theorem ◽  
Transitive Binary Relation

Motivated by the ideas of F -weak contractions and F , R g -contractions, the notion of F w , R g -contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for F w , R g -contractions in metric spaces equipped with a transitive binary relation. The results are elaborated by illustrative examples. Some consequences of these results are also deduced in ordered metric spaces and metric spaces endowed with graph. Finally, as an application, the existence of the solution of certain Voltera type integral equations is investigated.

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 Multivalued generalizations of fixed point results in fuzzy metric spaces

2016 ◽  
Vol 21 (2) ◽  
pp. 211-22 ◽  
Author(s):  
Tatjana Došenovic ◽  
Dušan Rakic ◽  
Biljana Caric ◽  
Stojan Radenovic
Keyword(s):  
Fixed Point ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Multivalued Mappings ◽  
Altering Distance Function ◽  
Fuzzy Metric ◽  
Altering Distance ◽  
Theoretical Results

This paper attempts to prove fixed and coincidence point results in fuzzy metric space using multivalued mappings. Altering distance function and multivalued strong {bn}-fuzzy contraction are used in order to do that. Presented theorems are generalization of some well known single valued results. Two examples are given to support the theoretical results.

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.

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