cone metric spaces
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Author(s):  
Abdullah Al-Yaari ◽  
Hamzah Sakidin ◽  
Yousif Alyousifi ◽  
Qasem Al-Tashi

This study involves new notions of continuity of mapping between quasi-cone metrics spaces (QCMSs), cone metric spaces (CMSs), and vice versa. The relation between all notions of continuity were thoroughly studied and supported with the help of examples. In addition, these new continuities were compared with various types of continuities of mapping between two QCMSs. The continuity types are 𝒇𝒇-continuous, 𝒃𝒃-continuous, 𝒇𝒃-continuous, and 𝒃𝒇-continuous. The results demonstrated that the new notions of continuity could be generalized to the continuity of mapping between two QCMSs. It also showed a fixed point for this continuity map between a complete Hausdorff CMS and QCMS. Overall, this study supports recent research results.


2021 ◽  
pp. 1-21
Author(s):  
Rashwan A. Rashwan ◽  
Hasanen A. Hammad ◽  
A. Nafea

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application.


2021 ◽  
Vol 6 (1) ◽  
pp. 16
Author(s):  
Adrian Nicolae Branga

In this paper, the concept of F-contraction was generalized for cone metric spaces over topological left modules and some fixed point results were obtained for self-mappings satisfying a contractive condition of this type. Some applications of the main result to the study of the existence and uniqueness of the solutions for certain types of integral equations were presented in the last part of the article, one of them being a fractional integral equation.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Saif Ur Rehman ◽  
Hawraa Akram Yazbek ◽  
Rashad A. R. Bantan ◽  
Mohammed Elgarhy

This paper is aimed at proving some unique common fixed point theorems by using the compatible and weakly-compatible four self-mappings in fuzzy cone metric (FCM) space. We prove the results under the generalized rational contraction conditions in FCM spaces with the help of one self-map are continuous. Furthermore, we prove some rational contraction results with the weaker condition of the self-mapping continuity. Ultimately, our theoretical work has been utilized to prove the existence solution of the two nonlinear integral equations. This is an illustrative application of how FCM spaces can be used in other integral type operators.


Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2267
Author(s):  
Hasanen A. Hammad ◽  
Manuel De la De la Sen

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anita Tomar ◽  
Meena Joshi

Abstract The convergence of sequences and non-unique fixed points are established in ℳ-orbitally complete cone metric spaces over the strongly mini-hedral cone, and scalar weighted cone assuming the cone to be strongly mini-hedral. Appropriate examples and applications validate the established theory. Further, we provide one more answer to the question of the existence of the contractive condition in Cone metric spaces so that the fixed point is at the point of discontinuity of a map. Also, we provide a negative answer to a natural question of whether the contractive conditions in the obtained results can be replaced by its metric versions.


2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Saif Ur Rehman ◽  
Muhammad Talha Waheed ◽  
Naeem Jan ◽  
Abdu Gumaei ◽  
Mabrook Al-Rakhami

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.


2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Muhammad Talha Waheed ◽  
Saif Ur Rehman ◽  
Naeem Jan ◽  
Abdu Gumaei ◽  
Mabrook Al-Rakhami

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.


2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Muhammad Talha Waheed ◽  
Saif Ur Rehman ◽  
Naeem Jan ◽  
Abdu Gumaei ◽  
Mabrook Al-Rakhami

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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