scholarly journals An Approach of Lebesgue Integral in Fuzzy Cone Metric Spaces via Unique Coupled Fixed Point Theorems

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Muhammad Talha Waheed ◽  
Saif Ur Rehman ◽  
Naeem Jan ◽  
Abdu Gumaei ◽  
Mabrook Al-Rakhami
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Lebesgue Integral ◽  
Cone Metric Spaces ◽  
Main Work ◽  
Contractive Type ◽  
Fuzzy Fixed Point ◽  
Cone Metric

In the theory of fuzzy fixed point, many authors have been proved different contractive type fixed point results with different types of applications. In this paper, we establish some new fuzzy cone contractive type unique coupled fixed point theorems (FP-theorems) in fuzzy cone metric spaces (FCM-spaces) by using “the triangular property of fuzzy cone metric” and present illustrative examples to support our main work. In addition, we present a Lebesgue integral type mapping application to get the existence result of a unique coupled FP in FCM-spaces to validate our work.

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 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 Some New Coupled Fixed-Point Findings Depending on Another Function in Fuzzy Cone Metric Spaces with Application

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Muhammad Talha Waheed ◽  
Saif Ur Rehman ◽  
Naeem Jan ◽  
Abdu Gumaei ◽  
Mabrook Al-Rakhami
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Volterra Integral Equations ◽  
Cone Metric Spaces ◽  
Common Solution ◽  
Contractive Type ◽  
Cone Metric

In this paper, we introduce the new concept of coupled fixed-point (FP) results depending on another function in fuzzy cone metric spaces (FCM-spaces) and prove some unique coupled FP theorems under the modified contractive type conditions by using “the triangular property of fuzzy cone metric.” Another function is self-mapping continuous, one-one, and subsequently convergent in FCM-spaces. In support of our results, we present illustrative examples. Moreover, as an application, we ensure the existence of a common solution of the two Volterra integral equations to uplift our work.

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