cone metric space
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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 ◽  
Vol 2021 (1) ◽  
Author(s):  
Andreea Fulga ◽  
Hojjat Afshari ◽  
Hadi Shojaat

AbstractIn this manuscript, we investigate the existence and uniqueness of a common fixed point for the self-mappings defined on quasi-cone metric space over a divisible Banach algebra via an auxiliary mapping ϕ.


2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Abba Auwalu ◽  
Evren Hinçal

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.


2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jerolina Fernandez ◽  
Neeraj Malviya ◽  
Vahid Parvaneh ◽  
Hassen Aydi ◽  
Babak Mohammadi

In the present paper, we define J -cone metric spaces over a Banach algebra which is a generalization of G p b -metric space ( G p b -MS) and cone metric space (CMS) over a Banach algebra. We give new fixed-point theorems assuring generalized contractive and expansive maps without continuity. Examples and an application are given at the end to support the usability of our results.


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