Relation-Theoretic Nonlinear Contractions in $$an~ {{\mathcal {F}}}$$-Metric Space and Applications

2020 ◽  
Author(s):  
Anita Tomar ◽  
Meena Joshi
Keyword(s):  
Metric Space ◽  
Nonlinear Contractions

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 Discussion on Some Recent Order-Theoretic Metrical Coincidence Theorems Involving Nonlinear Contractions

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Aftab Alam ◽  
Qamrul Haq Khan ◽  
Mohammad Imdad
Keyword(s):  
Metric Space ◽  
Contractive Mapping ◽  
Ordered Metric Space ◽  
Coincidence Theorems ◽  
Whole Space ◽  
Nonlinear Contractions

We prove some coincidence theorems involving a pair of self-mappingsfandgdefined on an ordered metric spaceXwhereinfisg-increasingφ-contractive mapping. In our results, neither the whole spaceXnor the range subspaces (f(X)org(X)) are required to be complete. Instead, we use the completeness of a subspace ofXsatisfying suitable conditions.

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 Probabilistic Generalized Metric Spaces and Nonlinear Contractions

2016 ◽  
Vol 49 (4) ◽  
Author(s):  
Abderrahim Mbarki ◽  
Rachid Naciri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Probabilistic Generalization ◽  
Generalized Metric ◽  
Contraction Condition ◽  
Nonlinear Contractions

AbstractWe give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition without the assumption that the space is Hausdorff.

scholarly journals Stability of Fixed Point Sets of a Class of Multivalued Nonlinear Contractions

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Chaitali Bandyopadhyay
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Hausdorff Distance ◽  
Multivalued Mappings ◽  
Limit Function ◽  
Point Sets ◽  
Nonlinear Contractions ◽  
Fixed Point Sets

We consider a problem of stability of fixed point sets for a sequence of multivalued mappings defined on a metric space converging to a limit function where the convergence is with respect to the Pompeiu-Hausdorff distance. The members of the sequence are assumed to be multivalued almost contractions. We show that the fixed point sets of this sequence of mappings are stable.

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.

Sign in / Sign up

Export Citation Format

Share Document