Fixed point theorems for a pair of single-valued operators in a metric space endowed with a reflexive relation

2017 ◽  
Vol 33 (3) ◽  
pp. 301-310
Author(s):  
MELANIA-IULIA DOBRICAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Uniqueness Theorems ◽  
Mixed Monotone Property ◽  
First Order ◽  
System Equation ◽  
Coupled Fixed Points

In this paper we provide some existence and uniqueness theorems for coupled fixed points for a pair of contractive operators satisfying a mixed monotone property, in a metric space endowed with a reflexive relation. An application to a first-order differential system equation with PBV conditions is also given to illustrate the utility of our results.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

scholarly journals Coupled Fixed Point Theorems with New Implicit Relations and an Application

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
G. V. R. Babu ◽  
P. D. Sailaja
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Implicit Relation ◽  
Coupled Fixed Points

We introduce two new classes of implicit relations S and S′ where S′ is a proper subset of S, and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010). We prove the existence of coupled fixed points for the maps satisfying an implicit relation in S. These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation S′, where S′⊂S. Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010) to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006). As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.

scholarly journals On Some Coupled Fixed Points of Generalized T-Contraction Mappings in a bv(s)-Metric Space and Its Application

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 129
Author(s):  
Reny George ◽  
Zoran D. Mitrović ◽  
Stojan Radenović
Keyword(s):  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Existence And Uniqueness Theorem ◽  
Convergence Criteria ◽  
Nonlinear Integral Equations ◽  
Weaker Conditions ◽  
Coupled Fixed Points

Common coupled fixed point theorems for generalized T-contractions are proved for a pair of mappings S:X×X→X and g:X→X in a bv(s)-metric space, which generalize, extend, and improve some recent results on coupled fixed points. As an application, we prove an existence and uniqueness theorem for the solution of a system of nonlinear integral equations under some weaker conditions and given a convergence criteria for the unique solution, which has been properly verified by using suitable example.

scholarly journals Fixed point theorems for twisted (α,β)-ψ-contractive type mappings and applications

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 605-615 ◽  
Author(s):  
Peyman Salimi ◽  
Calogero Vetro ◽  
Pasquale Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Complete Metric Space ◽  
Contractive Type

The purpose of this paper is to discuss the existence and uniqueness of fixed points for new classes of mappings defined on a complete metric space. The obtained results generalize some recent theorems in the literature. Several applications and interesting consequences of our theorems are also given.

scholarly journals Generalized Contractions to Coupled Fixed Point Theorems in Partially Ordered Metric Spaces

2020 ◽  
pp. 492-502 ◽  
Author(s):  
Rao, N. Seshagiri ◽  
Karusala Kalyani
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Mixed Monotone Property ◽  
Ordered Metric Spaces ◽  
Rational Type

The purpose of this paper is to establish some coupled fixed point theorems for a self mapping satisfying certain rational type contractions along with strict mixed monotone property in a metric space endowed with partial order. Also, we have given the result of existence and uniqueness of a coupled fixed point for the mapping. This result generalize and extend several well known results in the literature

scholarly journals Alpha- F -Convex Contraction Mappings in b -Metric Space and a Related Fixed Point Theorem

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Kitila Wirtu Geleta ◽  
Kidane Koyas Tola ◽  
Solomon Gebregiorgis Teweldemedhin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Contraction Mappings

In this paper, we establish fixed point theorems for α - F -convex contraction mappings in b -metric space and prove the existence and uniqueness of fixed points for such mappings. Our result extends and generalizes comparable results in the existing literature. Finally, we provide an example in support of our main finding.

scholarly journals Existence and uniqueness of solutions to a first-order differential equation via fixed point theorem in orthogonal metric space

2019 ◽  
pp. 123
Author(s):  
Madjid Eshaghi Gordji ◽  
Hasti Habibi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Order Differential Equation ◽  
The Other ◽  
Uniqueness Theorems ◽  
Uniqueness Of Solutions ◽  
First Order

In this paper, among the other things, we show that the solution of the first-orderdifferential equation is a fixed point of an integral operator from an orthogonal metric space into itself. This approach provides a new proof of the classical existence and uniqueness theorems of solutions to a first-order differential equation.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

Fixed point theorems for expansive mappings in Gp-metric spaces

2017 ◽  
Vol 26 (3) ◽  
pp. 297-308
Author(s):  
MELTEM KAYA ◽  
◽  
HASAN FURKAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Expansive Mapping ◽  
Partial Metric Spaces ◽  
Weak Compatibility

In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph

2016 ◽  
Vol 59 (01) ◽  
pp. 3-12 ◽  
Author(s):  
Monther Rashed Alfuraidan
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Orlicz Spaces ◽  
Multivalued Mappings ◽  
Linear Spaces ◽  
Modular Metric Spaces ◽  
Modular Spaces

Abstract We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. This paper can be seen as a generalization of Nadler and Edelstein’s fixed point theorems to modular metric spaces endowed with a graph.

Sign in / Sign up

Export Citation Format

Share Document