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].

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 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 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.

scholarly journals A fixed point theorem for generalized metric spaces

1996 ◽  
Vol 19 (3) ◽  
pp. 457-460 ◽  
Author(s):  
B. E. Rhoades
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Generalized Metric Spaces ◽  
Generalized Metric

In this paper we prove two fixed point theorems for the generalized metric spaces introduced by Dhage.

scholarly journals On Weak Contractive Cyclic Maps in Generalized Metric Spaces and Some Related Results on Best Proximity Points and Fixed Points

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Nonempty Intersection ◽  
Generalized Metric Spaces ◽  
Best Proximity Points ◽  
Generalized Metric ◽  
Cyclic Maps ◽  
Convergence Of Sequences ◽  
Composite Maps ◽  
Decreasing Functions

This paper discusses the properties of convergence of sequences to limit cycles defined by best proximity points of adjacent subsets for two kinds of weak contractive cyclic maps defined by composite maps built with decreasing functions with either the so-calledr-weaker Meir-Keeler orr,r0-stronger Meir-Keeler functions in generalized metric spaces. Particular results about existence and uniqueness of fixed points are obtained for the case when the sets of the cyclic disposal have a nonempty intersection. Illustrative examples are discussed.

Sign in / Sign up

Export Citation Format

Share Document