scholarly journals Covering properties of continua and mappings

2003 ◽  
Vol 74 (88) ◽  
pp. 115-120
Author(s):  
Janusz Charatonik
Keyword(s):  
Monotone Mappings ◽  
Covering Property ◽  
Covering Properties

It is known that monotone mappings preserve the covering property for continua Similar result is proved for having the covering property hereditarily. An example is constructed which shows that the two results cannot be extended to almost monotone mappings.

scholarly journals On Weak Vitali Covering Properties

1978 ◽  
Vol 21 (3) ◽  
pp. 339-345 ◽  
Author(s):  
B. S. Thomson
Keyword(s):  
Exact Solution ◽  
Orlicz Spaces ◽  
Covering Property ◽  
Intimate Connection ◽  
Differentiation Theory ◽  
Covering Properties ◽  
Necessary And Sufficient

There are now a number of Vitali covering properties which have been defined to handle problems arising in differentiation theory. Although some of these have received a unified treatment, as for example in the setting of Orlicz spaces in [1, p. 168], the underlying simplicity can be lost and the intimate connection with the original weak Vitali covering property of de Possel obscured. In this note we present an exposition of a family of covering properties and show how the original methods of de Possel in [4] can be pushed to provide an exact solution of the problem of determining necessary and sufficient covering properties for a basis which is known to differentiate a given class of integrals.

scholarly journals Generalized open sets and selection properties

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1485-1493 ◽  
Author(s):  
Ljubisa Kocinac
Keyword(s):  
Topological Space ◽  
Covering Property ◽  
Covering Properties ◽  
Selection Principles ◽  
Menger Property

We define and study new weak versions of the classical Menger covering property. For this we use ?-open and ?-open covers of a topological space. Relations of these properties with known weak versions of the Menger property are examined. In this way we complement the study of weak covering properties defined by selection principles.

Peripheral Covering Properties Imply Covering Properties

1968 ◽  
Vol 20 ◽  
pp. 257-263
Author(s):  
E. E. Grace
Keyword(s):  
Slight Variation ◽  
Covering Property ◽  
Moore Space ◽  
Covering Properties ◽  
Moore Spaces

Recently several papers (11; 12; 13; 14) have been published in which it is shown that a Moore space (normal, in one case) is metrizable if it has the peripheral version (in the sense defined below) of a certain covering property that was known to imply metrizability of Moore spaces. Each of these metrization theorems can be proved more easily by using a slight variation of the appropriate standard proof to show that such a space is collectionwise normal and hence (2, Theorem 10) metrizable. But this approach, as well as that followed in (11 ; 12; 13 ; 14), obscures the point that, in Moore spaces and in more general settings, the peripheral versions of these covering properties imply the covering properties.

ON FULL COVERING PROPERTIES

1980 ◽  
Vol 6 (1) ◽  
pp. 77 ◽  
Author(s):  
Thomson
Keyword(s):  
Covering Properties

Approximating the minimum-norm fixed point of pseudocontractive mappings

2015 ◽  
Vol 08 (02) ◽  
pp. 1550036
Author(s):  
H. Zegeye ◽  
O. A. Daman
Keyword(s):  
Fixed Point ◽  
Iterative Process ◽  
Convergence Result ◽  
Monotone Mappings ◽  
Minimum Norm ◽  
Nonlinear Operators ◽  
Linear Inverse Problems ◽  
Minimization Problems ◽  
Pseudocontractive Mappings ◽  
Convex Minimization Problems

We introduce an iterative process which converges strongly to the minimum-norm fixed point of Lipschitzian pseudocontractive mapping. As a consequence, convergence result to the minimum-norm zero of monotone mappings is proved. In addition, applications to convexly constrained linear inverse problems and convex minimization problems are included. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

scholarly journals A strong convergence theorem for a zero of the sum of a finite family of maximally monotone mappings

2020 ◽  
Vol 53 (1) ◽  
pp. 152-166 ◽  
Author(s):  
Getahun B. Wega ◽  
Habtu Zegeye ◽  
Oganeditse A. Boikanyo
Keyword(s):  
Strong Convergence ◽  
Approximation Method ◽  
Convergence Theorem ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Important Class ◽  
Numerical Example ◽  
Minimization Problems ◽  
Nonlinear Mappings

AbstractThe purpose of this article is to study the method of approximation for zeros of the sum of a finite family of maximally monotone mappings and prove strong convergence of the proposed approximation method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems and provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

Combinatorics of Thin Posets: Application to Monotone Covering Properties

Order ◽  
2010 ◽  
Vol 28 (2) ◽  
pp. 173-179 ◽  
Author(s):  
Maddalena Bonanzinga ◽  
Mikhail Matveev
Keyword(s):  
Covering Properties
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