scholarly journals Normed Ordered and -Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmed Al-Rawashdeh ◽  
Wasfi Shatanawi ◽  
Muna Khandaqji
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Cone Metric Space ◽  
Cone Metric Spaces ◽  
Ordered Space ◽  
Cone Metric

In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space , and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of , and we discuss their extension to . We introduce the notion of -metric spaces and characterize cone metric space. Afterwards, we get generalizations of notions of convergence and Cauchy theory. In particular, we get a fixed point theorem of a contractive mapping in -metric spaces. Finally, by extending the notion of a contractive sequence in a real-valued metric space, we show that in -metric spaces, a contractive sequence is Cauchy.

scholarly journals Fixed point theorem between cone metric space and quasi-cone metric space

2022 ◽  
Vol 25 (1) ◽  
pp. 540
Author(s):  
Abdullah Al-Yaari ◽  
Hamzah Sakidin ◽  
Yousif Alyousifi ◽  
Qasem Al-Tashi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Cone Metric Spaces ◽  
Research Results ◽  
Cone Metric

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.

Fixed point theorem for quasi-contractive mapping in partial cone metric space

2014 ◽  
Vol 26 (5-6) ◽  
pp. 1153-1159 ◽  
Author(s):  
Wajdi Chaker ◽  
Abdelaziz Ghribi ◽  
Aref Jeribi ◽  
Bilel Krichen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Contractive Mapping ◽  
Cone Metric Space ◽  
Partial Cone ◽  
Cone Metric

scholarly journals Remarks on Some Recent Fixed Point Results on Quaternion-Valued Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Hamed H. Alsulami ◽  
Erdal Karapınar ◽  
Farshid Khojasteh
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Cone Metric Spaces ◽  
Fixed Point Result ◽  
Common Fixed Point Theorem ◽  
Cone Metric

Very recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. In this paper, we will show that the quaternion-valued metric spaces are subspaces of cone metric spaces. Consequently, the fixed point results in such spaces can be derived as a consequence of the corresponding existing fixed point result in the setting cone metric spaces.

scholarly journals On Complete Cone Metric Space and Fixed Point Theorem

2011 ◽  
Vol 3 (2) ◽  
pp. 303-309
Author(s):  
J. Mehta ◽  
M. L. Joshi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Weakly Compatible Maps ◽  
Cone Metric Spaces ◽  
Weakly Compatible ◽  
Contractive Type ◽  
Cone Metric

We prove coincidence and common fixed point theorems of four self mappings satisfying a generalized contractive type condition in complete cone metric spaces. Our results generalize some well-known recent results.Keywords: Common fixed point; Complete cone metric space; Weakly compatible maps.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.6475                J. Sci. Res. 3 (2), 303-309 (2011)

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 Fixed Point Theorems in Intuitionistic Generalized Fuzzy Cone Metric Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1212
Author(s):  
Mathuraiveeran Jeyaraman ◽  
Mookiah Suganthi ◽  
Wasfi Shatanawi
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Cone Metric

In the present work, we study many fixed point results in intuitionistic generalized fuzzy cone metric space. Precisely, we prove new common fixed point theorems for three self mappings that do not require any commutativity or continuity but a generalized contractive condition. Our results are generalizations for many results in the literature. Some examples are given to support these results.

scholarly journals Pentagonal Cone b-metric Spaces over Banach Algebras and Fixed Point Theorem of Generalized Lipschitz Mapping

2018 ◽  
Vol 22 ◽  
pp. 01003 ◽  
Author(s):  
Abba Auwalu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Lipschitz Mapping ◽  
Banach Fixed Point Theorem ◽  
Cone Metric ◽  
Generalized Lipschitz Mapping

In this paper, we introduce the concept of pentagonal cone b-metric space over Banach algebras as a generalization of cone metric space over Banach algebras and many of its generalizations. Furthermore, we prove Banach fixed point theorem in such a space. Our result unify, complement and/or generalized some recent results in the papers [1–7], and many others. We provide some examples to elucidate the validity and superiority of our results.

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