scholarly journals An application of a fixed point theorem in cone metric spaces for solving differential equations

2013 ◽  
Vol 22 (1) ◽  
pp. 65-71
Author(s):  
MONICA LAURAN ◽  
◽  
ANDREI HORVAT-MARC ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Third Order ◽  
Cone Metric Spaces ◽  
Cone Metric

In this paper we establish sufficient conditions for the existence and uniqueness of solutions for third order differential equations using a fixed point theorem in cone metric space. The presented result is based on some properties of invertible operators and extends several well-known comparable results in the literature.

scholarly journals The Existence of Cone Critical Point and Common Fixed Point with Applications

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Wei-Shih Du
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Critical Point ◽  
Point Theorem ◽  
Metric Spaces ◽  
Nonlinear Dynamical Systems ◽  
Cone Metric Spaces ◽  
Nonlinear Dynamical ◽  
Cone Metric

We first establish some new critical point theorems for nonlinear dynamical systems in cone metric spaces or usual metric spaces, and then we present some applications to generalizations of Dancš-Hegedüs-Medvegyev's principle and the existence theorem related with Ekeland's variational principle, Caristi's common fixed point theorem for multivalued maps, Takahashi's nonconvex minimization theorem, and common fuzzy fixed point theorem. We also obtain some fixed point theorems for weakly contractive maps in the setting of cone metric spaces and focus our research on the equivalence between scalar versions and vectorial versions of some results of fixed point and others.

scholarly journals BANACH FIXED POINT THEOREM ON ORTHOGONAL CONE METRIC SPACES

2021 ◽  
pp. 1239
Author(s):  
Zeinab Eivazi Damirchi Darsi Olia ◽  
Madjid Eshaghi Gordji ◽  
Davood Ebrahimi Bagha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solution ◽  
Banach Fixed Point Theorem ◽  
Cone Metric Spaces ◽  
Cone Metric

In this paper, we introduce new concept of orthogonal cone metric spaces. We stablish new versions of fixed point theorems in incomplete orthogonal cone metric spaces. As an application, we show the existence and uniqueness of solution of the periodic boundry value problem.

scholarly journals Fixed point theorem between cone metric space and quasi-cone metric space

2022 ◽  
Vol 25 (1) ◽  
pp. 540
Author(s):  
Abdullah Al-Yaari ◽  
Hamzah Sakidin ◽  
Yousif Alyousifi ◽  
Qasem Al-Tashi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Cone Metric Spaces ◽  
Research Results ◽  
Cone Metric

This study involves new notions of continuity of mapping between quasi-cone metrics spaces (QCMSs), cone metric spaces (CMSs), and vice versa. The relation between all notions of continuity were thoroughly studied and supported with the help of examples. In addition, these new continuities were compared with various types of continuities of mapping between two QCMSs. The continuity types are 𝒇𝒇-continuous, 𝒃𝒃-continuous, 𝒇𝒃-continuous, and 𝒃𝒇-continuous. The results demonstrated that the new notions of continuity could be generalized to the continuity of mapping between two QCMSs. It also showed a fixed point for this continuity map between a complete Hausdorff CMS and QCMS. Overall, this study supports recent research results.

scholarly journals Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

2018 ◽  
Vol 1 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Mısır J. Mardanov ◽  
Yagub A. Sharifov ◽  
Kamala E. Ismayilova
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractThis paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer’s fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.

scholarly journals Theta Cone Metric Spaces and Some Fixed Point Theorems

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Sahar Mohamed Ali Abou Bakr
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Properties ◽  
Cone Metric Spaces ◽  
Cone Metric

This paper introduces the concept of the theta cone metric, studies its various topological properties, and gives some examples of it. Furthermore, it proves some lemmas and then uses them to give further generalizations of some well-known fixed point theorems. Specifically, Theorem 2 of the paper is a generalization of Reich’s fixed point theorem.

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