scholarly journals Fixed Point Theorems of Quasicontractions on Cone Metric Spaces with Banach Algebras

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hao Liu ◽  
Shaoyuan Xu
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Algebras ◽  
New Method ◽  
Cone Metric Spaces ◽  
Cone Metric

We introduce the concept of quasicontractions on cone metric spaces with Banach algebras, and by a new method of proof, we will prove the existence and uniqueness of fixed points of such mappings. The main result generalizes the well-known theorem of Ćirić (Ćirić 1974).

scholarly journals Fixed Point Results for Weakφ-Contractions in Cone Metric Spaces over Banach Algebras and Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Biwen Li ◽  
Huaping Huang
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Spaces ◽  
Uniqueness Of A Solution ◽  
Cone Metric

By using a nontrivial proof method, the purpose of this paper is to obtain some fixed point results for weakφ-contractions in cone metric spaces over Banach algebras. Several examples and applications to the existence and uniqueness of a solution to two classes of equations are also given.

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 Unique common fixed points for mixed contractive mappings on non-normal cone metric spaces over Banach algebras

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2067-2079
Author(s):  
Yongjie Piao ◽  
Shaoyuan Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Normal Cone ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Common Fixed Points ◽  
Cone Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Cone Metric ◽  
Unique Common Fixed Point

In this paper, we discuss and obtain some new unique common fixed point theorems for two mappings satisfying Kannan type mixed contractive conditions and Chatterjea type mixed contractive conditions respectively on cone metric spaces over Banach algebras without the assumption of normality and give some generalizations of Kannan type and Chatterjea type fixed point theorems.

scholarly journals Fixed point Theorems for Non-self mappings with nonlinear contractive condition in strictly convex FCM-spaces

2020 ◽  
Vol 26 (1) ◽  
pp. 1-21
Author(s):  
Mohammad H.M. Rashid
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Strictly Convex ◽  
Convex Structure ◽  
Cone Metric

In this paper we define convex, strict convex and normal structures for sets in fuzzy cone metric spaces. Also, existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition will be proved, using the notion of strictly convex structure. Moreover, we give some examples illustrate our results.

scholarly journals Some Fixed Point Theorems of Contractive Mappings in P b r -Cone Metric Spaces over Banach Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Abba Auwalu ◽  
Evren Hinçal
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Cone Metric Space ◽  
Cone Metric Spaces ◽  
Contractive Mappings ◽  
Cone Metric

In this paper, we introduce the concept of a P b r -cone metric space over Banach algebras and prove some fixed point results under various contractive mappings in such a space. Some examples are given to elucidate the results. Our results extend and generalize many existing results in the literature.

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.

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