scholarly journals Common Coupled Fixed Point Theorems of Single-Valued Mapping forc-Distance in Cone Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Zaid Mohammed Fadail ◽  
Abd Ghafur Bin Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Cone Metric Spaces ◽  
Common Coupled Fixed Point ◽  
Different Types ◽  
The Common ◽  
Contraction Type ◽  
Cone Metric

The existence and uniqueness of the common coupled fixed point in cone metric spaces have been studied by considering different types of contractive conditions. A new concept of thec-distance in cone metric space has been recently introduced in 2011. Then, coupled fixed point results for contraction-type mappings in ordered cone metric spaces and cone metric spaces have been considered. In this paper, some common coupled fixed point results onc-distance in cone metric spaces are obtained. Some supporting examples are given.

scholarly journals $FG$-coupled fixed point theorems in cone metric spaces

2018 ◽  
Vol 9 (2) ◽  
pp. 163-170
Author(s):  
E. Prajisha ◽  
P. Shaini
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Cone Metric Spaces ◽  
Contraction Type ◽  
Cone Metric

The concept of $FG$- coupled fixed point introduced recently is a generalization of coupled fixed point introduced by Guo and Lakshmikantham. A point $(x,y)\in X\times X$ is said to be a coupled fixed point of the mapping $F: X\times X \rightarrow X$ if $F(x,y)=x$ and $F(y,x)=y$, where $X$ is a non empty set. In this paper, we introduce $FG$- coupled fixed point in cone metric spaces for the mappings $F:X\times Y \rightarrow X$ and $G:Y\times X\rightarrow Y$ and establish some $FG$- coupled fixed point theorems for various mappings such as contraction type mappings, Kannan type mappings and Chatterjea type mappings. All the theorems assure the uniqueness of $FG$- coupled fixed point. Our results generalize several results in literature, mainly the coupled fixed point theorems established by Sabetghadam et al. for various contraction type mappings. An example is provided to substantiate the main theorem.

scholarly journals Coupled Fixed Point Theorems of Single-Valued Mapping forc-Distance in Cone Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Zaid Mohammed Fadail ◽  
Abd Ghafur Bin Ahmad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Cone Metric Space ◽  
Cone Metric Spaces ◽  
Cone Metric

A new concept of thec-distance in cone metric space has been introduced recently in 2011. The aim of this paper is to extend and generalize some coupled fixed-point theorems onc-distance in cone metric space. Some examples are given.

scholarly journals Coupled Fixed Point Theorems under Weak Contractions

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Y. J. Cho ◽  
Z. Kadelburg ◽  
R. Saadati ◽  
W. Shatanawi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Cone Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Cone Metric

Cho et al. [Comput. Math. Appl. 61(2011), 1254–1260] studied common fixed point theorems on cone metric spaces by using the concept ofc-distance. In this paper, we prove some coupled fixed point theorems in ordered cone metric spaces by using the concept ofc-distance in cone metric spaces.

scholarly journals Some Rational Coupled Fuzzy Cone Contraction Theorems in Fuzzy Cone Metric Spaces with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Saif Ur Rehman ◽  
Muhammad Talha Waheed ◽  
Naeem Jan ◽  
Abdu Gumaei ◽  
Mabrook Al-Rakhami
Keyword(s):  
Fixed Point ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Integral Type ◽  
Cone Metric Spaces ◽  
Cone Metric ◽  
Rational Type ◽  
Type Contraction

In this paper, we establish the new concept of rational coupled fuzzy cone contraction mapping in fuzzy cone metric spaces and prove some unique rational-type coupled fixed-point theorems in the framework of fuzzy cone metric spaces by using “the triangular property of fuzzy cone metric.” To ensure the existence of our results, we present some illustrative unique coupled fixed-point examples. Furthermore, we present an application of a Lebesgue integral-type contraction mapping in fuzzy cone metric spaces and to prove a unique coupled fixed-point theorem.

scholarly journals Some Coupled Fixed Point Theorems in Cone Metric Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
F. Sabetghadam ◽  
H. P. Masiha ◽  
A. H. Sanatpour
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Cone Metric Spaces ◽  
Cone Metric

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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