scholarly journals Fixed Point Theorems in Quaternion-Valued Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Ahmed El-Sayed Ahmed ◽  
Saleh Omran ◽  
Abdalla J. Asad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Normal Cone ◽  
Metric Spaces ◽  
Cone Metric Spaces ◽  
Contraction Condition ◽  
General Contraction ◽  
Cone Metric

The aim of this paper is twofold. First, we introduce the concept of quaternion metric spaces which generalizes both real and complex metric spaces. Further, we establish some fixed point theorems in quaternion setting. Secondly, we prove a fixed point theorem in normal cone metric spaces for four self-maps satisfying a general contraction condition.

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 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.

scholarly journals Fixed Point Theorems in Complete Cone Metric Spaces over Banach Algebras

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Seong-Hoon Cho
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Weak Contraction ◽  
Cone Metric Spaces ◽  
Contraction Type ◽  
Cone Metric

The notion of C-class functions in Banach algebras is introduced. By using such concept, a new fixed point theorem is established. An example to illustrate main theorem is given. Finally, applications of our main result to cyclic mappings and weak contraction type mappings are given.

scholarly journals Some Nonunique Fixed Point Theorems of Ćirić Type on Cone Metric Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Spaces ◽  
Cone Metric

Some results of (Ćirić, 1974) on a nonunique fixed point theorem on the class of metric spaces are extended to the class of cone metric spaces. Namely, nonunique fixed point theorem is proved in orbitally complete cone metric spaces under the assumption that the cone is strongly minihedral. Regarding the scalar weight of cone metric, we are able to remove the assumption of strongly minihedral.

scholarly journals Coupled Fixed-Point Theorems in Theta-Cone-Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Sahar Mohamed Ali Abou Bakr
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Cone Metric Spaces ◽  
Underlying Space ◽  
Coupled Fixed Point Theorem ◽  
Cone Metric

This paper gives further generalizations of some well-known coupled fixed-point theorems. Specifically, Theorem 3 of the paper is the generalization of the Baskar–Lackshmikantham coupled fixed-point theorem, and Theorem 5 is the generalization of the Sahar Mohamed Ali Abou Bakr fixed-point theorem, where the underlying space is complete θ -cone-metric space.

Fixed point theorems for nonself Bianchini type contractions in Banach spaces endowed with a graph

2018 ◽  
Vol 27 (1) ◽  
pp. 37-48
Author(s):  
ANDREI HORVAT-MARC ◽  
◽  
LASZLO BALOG ◽  
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contraction Condition

In this paper we present an extension of fixed point theorem for self mappings on metric spaces endowed with a graph and which satisfies a Bianchini contraction condition. We establish conditions which ensure the existence of fixed point for a non-self Bianchini contractions T : K ⊂ X → X that satisfy Rothe’s boundary condition T (∂K) ⊂ K.

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.

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