scholarly journals Topologies on Superspaces of TVS-Cone Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xun Ge ◽  
Shou Lin
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Vietoris Topology ◽  
Cone Metric Spaces ◽  
Nonempty Compact ◽  
Cone Metric ◽  
Compact Subsets

This paper investigates superspaces𝒫0(X)and𝒦0(X)of a tvs-cone metric space(X,d), where𝒫0(X)and𝒦0(X)are the space consisting of nonempty subsets ofXand the space consisting of nonempty compact subsets ofX, respectively. The purpose of this paper is to establish some relationships between the lower topology and the lower tvs-cone hemimetric topology (resp., the upper topology and the upper tvs-cone hemimetric topology to the Vietoris topology and the Hausdorff tvs-cone hemimetric topology) on𝒫0(X)and𝒦0(X), which makes it possible to generalize some results of superspaces from metric spaces to tvs-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 New Fixed Point Results of Single-Valued Mapping forc-Distance in Cone Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Zaid Mohammed Fadail ◽  
Abd Ghafur Bin Ahmad ◽  
Ljiljana Paunović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
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 fixed point results in literature forc-distance in cone metric spaces by replacing the constants in contractive conditions with functions. Some supporting examples are given.

scholarly journals On J -Cone Metric Spaces over a Banach Algebra and Some Fixed-Point Theorems

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jerolina Fernandez ◽  
Neeraj Malviya ◽  
Vahid Parvaneh ◽  
Hassen Aydi ◽  
Babak Mohammadi
Keyword(s):  
Fixed Point ◽  
Banach Algebra ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Cone Metric Spaces ◽  
Expansive Maps ◽  
Cone Metric

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.

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.

scholarly journals Φ,Ψ-Weak Contractions in Neutrosophic Cone Metric Spaces via Fixed Point Theorems

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Wadei F. Al-Omeri ◽  
Saeid Jafari ◽  
Florentin Smarandache
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Space ◽  
Weak Contraction ◽  
Cone Metric Spaces ◽  
Altering Distance ◽  
Common Fixed Point Theorems ◽  
Cone Metric

In this manuscript, we obtain common fixed point theorems in the neutrosophic cone metric space. Also, notion of Φ,Ψ-weak contraction is defined in the neutrosophic cone metric space by using the idea of altering distance function. Finally, we review many examples of cone metric spaces to verify some properties.

scholarly journals Fixed Point Theorems of Single-Valued Mapping forc-Distance in Cone Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Zaid Mohammed Fadail ◽  
Abd Ghafur Bin Ahmad ◽  
Zoran Golubović
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
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 fixed point theorems onc-distance in cone metric space.

scholarly journals Slowly oscillating continuity in abstract metric spaces

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 925-930 ◽  
Author(s):  
Hüseyin Çakallı ◽  
Ayșe Sӧnmez
Keyword(s):  
Vector Space ◽  
Compact Subset ◽  
Topological Vector Space ◽  
Metric Space ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Cone Metric Space ◽  
Cone Metric Spaces ◽  
Uniformly Continuous ◽  
Cone Metric

In this paper, we investigate slowly oscillating continuity in cone metric spaces. It turns out that the set of slowly oscillating continuous functions is equal to the set of uniformly continuous functions on a slowly oscillating compact subset of a topological vector space valued cone metric space.

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