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 Fixed Point Theorems of Integral Type Contraction in Cone Metric Spaces

2010 ◽  
Vol 2010 (1) ◽  
pp. 189684 ◽  
Author(s):  
Farshid Khojasteh ◽  
Zahra Goodarzi ◽  
Abdolrahman Razani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Integral Type ◽  
Cone Metric Spaces ◽  
Cone Metric ◽  
Type Contraction

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 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 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 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 Some Novel Generalized Strong Coupled Fixed Point Findings in Cone Metric Spaces with Application to Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Saif Ur Rehman ◽  
Sami Ullah Khan ◽  
Abdul Ghaffar ◽  
Shao-Wen Yao ◽  
Mustafa Inc
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Applied Mathematics ◽  
Coupled Fixed Point ◽  
Cone Metric Spaces ◽  
Common Solution ◽  
Contractive Type ◽  
Cone Metric ◽  
Type Contraction

Fixed point (FP) has been the heart of several areas of mathematics and other sciences. FP is a beautiful mixture of analysis (pure and applied), topology, and geometry. To construct the link between FP and applied mathematics, this paper will present some generalized strong coupled FP theorems in cone metric spaces. Our consequences give the generalization of “cyclic coupled Kannan-type contraction” given by Choudhury and Maity. We present illustrative examples in support of our results. This new concept will play an important role in the theory of fixed point results and can be generalized for different contractive-type mappings in the context of metric spaces. In addition, we also establish an application in integral equations for the existence of a common solution to support our work.

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