Hyers–Ulam stability for coupled random fixed point theorems and applications to periodic boundary value random problems

2019 ◽  
Vol 27 (3) ◽  
pp. 143-152
Author(s):  
A. Boudaoui ◽  
T. Caraballo ◽  
T. Blouhi
Keyword(s):  
Fixed Point ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Boundary Value ◽  
Ulam Stability ◽  
Random Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Type ◽  
Stability Results

Abstract In this paper, we prove some existence, uniqueness and Hyers–Ulam stability results for the coupled random fixed point of a pair of contractive type random operators on separable complete metric spaces. The approach is based on a new version of the Perov type fixed point theorem for contractions. Some applications to integral equations and to boundary value problems are also given.

scholarly journals Random fixed point theorems for contractive type multifunctions

2005 ◽  
Vol 78 (2) ◽  
pp. 211-220 ◽  
Author(s):  
Ghulam Mustafa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coincidence Point ◽  
Multivalued Mappings ◽  
Random Coincidence ◽  
Random Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Type

AbstractSome new random coincidence point and random fixed point theorems for multivalued mappings in separable complete metric spaces are proved. The results presented in this paper are the stochastic versions of corresponding results of Chang and Peng and extend the result of the author.

Ulam-Hyers stability theorem by tripled fixed point theorem

2016 ◽  
Vol 56 (1) ◽  
pp. 77-97
Author(s):  
Animesh Gupta
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Stability Theorem ◽  
Tripled Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Type ◽  
Vector Valued ◽  
Stability Results

AbstractThis paper deals with tripled fixed point theorem, and the approach is based on Perov-type fixed point theorem for contractions in metric spaces endowed with vector-valued metrics. We are also study Ulam-Hyers stability results for the tripled fixed points of a triple of contractive type single-valued and respectively multi-valued operators on complete metric spaces.

scholarly journals An Application of Fixed Point Theory to a Nonlinear Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. P. Farajzadeh ◽  
A. Kaewcharoen ◽  
S. Plubtieng
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Nonlinear Differential Equation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Complete Metric Spaces ◽  
New Family ◽  
Contractive Type

We introduce a new family of mappings on[0,+∞)by relaxing the nondecreasing condition on the mappings and by using the properties of this new family we present some fixed point theorems forα-ψ-contractive-type mappings in the setting of complete metric spaces. By applying our obtained results, we also assure the fixed point theorems in partially ordered complete metric spaces and as an application of the main results we provide an existence theorem for a nonlinear differential equation.

scholarly journals Fixed Point Theorems for a Class ofα-Admissible Contractions and Applications to Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hamed H. Alsulami ◽  
Selma Gülyaz ◽  
Erdal Karapınar ◽  
İncı M. Erhan
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Distance Functions ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Altering Distance

A class ofα-admissible contractions defined via altering distance functions is introduced. The existence and uniqueness conditions for fixed points of such maps on complete metric spaces are investigated and related fixed point theorems are presented. The results are reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions.

scholarly journals Fixed points of multivalued nonexpansive maps

1991 ◽  
Vol 14 (3) ◽  
pp. 421-430 ◽  
Author(s):  
T. Husain ◽  
Abdul Latif
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Nonexpansive Maps ◽  
Contractive Type ◽  
Bounded Convex ◽  
Convex Subsets

Fixed point theorems for multivalued contractive-type and nonexpansive-type maps on complete metric spaces and on certain closed bounded convex subsets of Banach spaces have been proved. They extend some known results due to Browder, Husain and Tarafdar, Karlovitz and Kirk.

scholarly journals Some common random fixed point theorems for contractive type conditions in cone random metric spaces

2016 ◽  
Vol 8 (1) ◽  
pp. 174-190 ◽  
Author(s):  
Gurucharan S. Saluja ◽  
Bhanu Pratap Tripathi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Random Fixed Point ◽  
Contractive Type

AbstractIn this paper, we establish some common random fixed point theorems for contractive type conditions in the setting of cone random metric spaces. Our results unify, extend and generalize many known results from the current existing literature.

scholarly journals αH-ψH-Multivalued Contractive Mappings and Related Results in Complete Metric Spaces with An Application

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 68
Author(s):  
Pooja Dhawan ◽  
Kapil Jain ◽  
Jatinderdeep Kaur
Keyword(s):  
Fixed Point ◽  
Present Article ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Multivalued Contraction ◽  
Contractive Mappings ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Homotopy Result

In the present article, the notion of αH-ψH-multivalued contractive type mappings is introduced and some fixed point results in complete metric spaces are studied. These theorems generalize Nadler’s (Multivalued contraction mappings, Pac. J. Math., 30, 475–488, 1969) and Suzuki-Kikkawa's (Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal., 69, 2942–2949, 2008) results that exist in the literature. The effectiveness of the obtained results has been verified with the help of some comparative examples. Moreover, a homotopy result has been presented as an application.

scholarly journals Existence of Solutions for a Periodic Boundary Value Problem via Generalized Weakly Contractions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sirous Moradi ◽  
Erdal Karapınar ◽  
Hassen Aydi
Keyword(s):  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Weakly Contractive

We discuss the existence of solutions for a periodic boundary value problem and for some polynomials. For this purpose, we present some fixed point theorems for weakly and generalized weakly contractive mappings in the setting of partially ordered complete metric spaces.

scholarly journals Tripled fixed point theorems for monotone mappings in partially ordered metric spaces

2012 ◽  
Vol 28 (2) ◽  
pp. 215-222
Author(s):  
MARIN BORCUT ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Monotone Mappings ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Contractive Type

In this paper, we introduce the concept of tripled fixed point for nonlinear and monotone mappings in partially ordered complete metric spaces and obtain existence as well as existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent tripled fixed point theorems established by Berinde and Borcut [Berinde, V., Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces. Nonlinear Anal. 74 (2011) 4889–4897]. Examples to support our new results are given.

scholarly journals Common Fixed Point Theorems for α-ψ-Contractive Type Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jalal Hassanzadeasl
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Common Fixed Points ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
Contractive Type ◽  
Common Fixed Point Theorems

Recently, Samet et al. (2012) introduced the notion of α-ψ-contractive type mappings. They established some fixed point theorems for these mappings in complete metric spaces. In this paper, we introduce the notion of a coupled α-ψ-contractive mapping and give a common fixed point result about the mapping. Also, we give a result of common fixed points of some coupled self-maps on complete metric spaces satisfying a contractive condition.

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