scholarly journals The Characterization of Generalized Metric KKM Mappings with Open Values in Hyperconvex Metric Spaces and Some Applications

1999 ◽  
Vol 235 (1) ◽  
pp. 315-325 ◽  
Author(s):  
George Xian-Zhi Yuan
Keyword(s):  
Metric Spaces ◽  
Generalized Metric ◽  
Kkm Mappings

Characterization of Certain Classes of Spaces With Gδ Points as Open Images of Metric Spaces

1975 ◽  
Vol 27 (6) ◽  
pp. 1229-1238
Author(s):  
Kenneth C. Abernethy
Keyword(s):  
Metric Spaces ◽  
Topological Spaces ◽  
Generalized Metric Spaces ◽  
The Past ◽  
Generalized Metric

The study of metrization has led to the development of a number of new topological spaces, called generalized metric spaces, within the past fifteen years. For a survey of results in metrization theory involving many of these spaces, the reader is referred to [13]. Quite a few of these generalized metric spaces have been studied extensively, somewhat independently of their role in metrization theorems. Specifically, we refer here to characterizations of these spaces by various workers as images of metric spaces. Results in this area have been obtained by Alexander [2], Arhangel'skii [3], Burke [5], Heath [10], Michael [15], Nagata [16], and the author [1], to mention a few. Later we will recall specifically some of these results.

scholarly journals Measures of noncompactness on w-distance spaces

2021 ◽  
Vol 25 (1) ◽  
pp. 63-69
Author(s):  
Aleksandar Kostić
Keyword(s):  
Measure Of Noncompactness ◽  
Metric Spaces ◽  
Measures Of Noncompactness ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Open Question ◽  
Phd Thesis ◽  
New Framework

The aim of this paper is to provide a new framework for the study of measures of noncompactness in generalized metric spaces. Firstly, we introduce the notion of w-measure of noncompactness on metric spaces with a w-distance and extend the diameter and Kuratowski functionals to this setting. At the end we give a characterization of metric completeness via our main results, providing a new answer to the open question mentioned by Arandjelović in his PhD thesis [2].

scholarly journals A characterization of completeness of generalized metric spaces using generalized Banach contraction principle

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
Piu Ghosh ◽  
A. Deb Ray
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Metric Spaces ◽  
Contraction Principle ◽  
Generalized Metric Space ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Banach Contraction ◽  
Banach’S Fixed Point Theorem

AbstractIn this paper, introducing a contraction principle on generalized metric spaces, a generalization of Banach’s fixed point theorem is obtained under the completeness condition of the space. Moreover, it is established that, using such contraction principle, completeness of the generalized metric space can be characterized.

scholarly journals Knaster-Kuratowski-Mazurkiewicz Theorem in Generalized Metric Spaces with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Nayyar Mehmood ◽  
Israr Ali Khan ◽  
Haris Latif ◽  
Niaz Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fixed Points ◽  
Existence Result ◽  
Metric Spaces ◽  
Fractional Boundary Value Problem ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Kkm Mappings

We study Knaster-Kuratowski-Mazurkiewicz theorem in the setting of generalized metric spaces. We establish some results on fixed points of Knaster-Kuratowski-Mazurkiewicz (KKM) mappings. Fan’s matching and Schauder’s type fixed point theorem in generalized metric spaces are also proved as interesting consequences of our main results. Examples are given to validate our results. We use these results to prove existence result for a given Atangana-Baleanu-Caputo fractional boundary value problem.

scholarly journals Improving KKM Theory on General Metric Type Spaces

2021 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
Sehie Park
Keyword(s):  
Convex Space ◽  
Metric Spaces ◽  
Space Theory ◽  
Type Space ◽  
Generalized Metric ◽  
Abstract Convex Space ◽  
Type Spaces

Abstract A generalized metric type space is a generic name for various spaces similar to hyperconvex metric spaces or extensions of them. The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work or some contents, and add some comments showing how to improve them.

scholarly journals An Intrinsic Characterization of Five Points in a CAT(0) Space

2020 ◽  
Vol 8 (1) ◽  
pp. 114-165
Author(s):  
Tetsu Toyoda
Keyword(s):  
Metric Space ◽  
Isometric Embedding ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
New Approach ◽  
Intrinsic Characterization ◽  
New Family

AbstractGromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space.

scholarly journals Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dušan Ðukić ◽  
Zoran Kadelburg ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces ◽  
Type Spaces

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

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