Fixed point results for multivalued operators with respect to a c - distance

2015 ◽  
Vol 31 (2) ◽  
pp. 221-232
Author(s):  
ENRIQUE LLORENS-FUSTER ◽  
◽  
CRISTINA URS ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Cone Metric Spaces ◽  
Multivalued Operators ◽  
Contractive Type ◽  
Cone Metric

In this paper we present a fixed point theorem for contractive type multivalued operators in cone metric spaces by using the concept of c-distance.

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 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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