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 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.

The Brachistochrone With a Movable End-Point and the Nonsimultaneous Variations

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
D. Radomirovic ◽  
Dj. Djukic ◽  
L. Cveticanin
Keyword(s):  
Exact Solution ◽  
Calculus Of Variations ◽  
Parametric Method ◽  
Sufficient Conditions ◽  
Integral Type ◽  
First Order ◽  
End Point ◽  
Order Variation ◽  
Ritz’S Method ◽  
Necessary And Sufficient

In this paper, the necessary and sufficient conditions for minima plane path with a movable end-point are developed. Using the calculus of variations the considered conditions are based on the zero first-order nonsimultaneous variation and on the positive second-order variation in the functional of integral type corresponding to mechanical systems. The applied procedure is the coordinate parametric method. The obtained solutions are tested on a brachistochrone with one end-point constrained to lie on a circle. The exact solution is compared with the approximate one obtained with Ritz’s method.

scholarly journals The Schur and (weak) Dunford-Pettis properties in Banach lattices

2002 ◽  
Vol 73 (2) ◽  
pp. 251-278 ◽  
Author(s):  
Anna Kamińska ◽  
Mieczysław Mastyło
Keyword(s):  
Orlicz Spaces ◽  
Sufficient Conditions ◽  
Complete Characterization ◽  
Sequence Spaces ◽  
Banach Lattices ◽  
Schur Property ◽  
Atomic Measure ◽  
Orlicz Sequence Spaces ◽  
Necessary And Sufficient

AbstractWe study the Schur and (weak) Dunford-Pettis properties in Banach lattices. We show that l1, c0 and l∞ are the only Banach symmetric sequence spaces with the weak Dunford-Pettis property. We also characterize a large class of Banach lattices without the (weak) Dunford-Pettis property. In MusielakOrlicz sequence spaces we give some necessary and sufficient conditions for the Schur property, extending the Yamamuro result. We also present a number of results on the Schur property in weighted Orlicz sequence spaces, and, in particular, we find a complete characterization of this property for weights belonging to class ∧. We also present examples of weighted Orlicz spaces with the Schur property which are not L1-spaces. Finally, as an application of the results in sequence spaces, we provide a description of the weak Dunford-Pettis and the positive Schur properties in Orlicz spaces over an infinite non-atomic measure space.

scholarly journals Criterion for the Coincidence of Strong and Weak Orlicz Spaces

2021 ◽  
Vol 58 (3) ◽  
pp. 381-397
Author(s):  
Maria Rosaria Formica ◽  
Eugeny Ostrovsky
Keyword(s):  
Orlicz Spaces ◽  
Sufficient Conditions ◽  
Norm Inequality ◽  
Necessary And Sufficient Conditions ◽  
Embedding Constant ◽  
Necessary And Sufficient

We provide necessary and sufficient conditions for the coincidence, up to equivalence of the norms, between strong and weak Orlicz spaces. Roughly speaking, this coincidence holds true only for the so-called exponential spaces. We also find the exact value of the embedding constant which appears in the corresponding norm inequality.

scholarly journals Viewing *-multiplication operators between Orlicz spaces

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2185-2191
Author(s):  
Jahangir Cheshmavar ◽  
Seyed Hosseini
Keyword(s):  
Conditional Expectation ◽  
Orlicz Spaces ◽  
Multiplication Operators ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Closed Range ◽  
Necessary And Sufficient

In this paper, Lambert multipliers acting between Orlicz spaces are characterized based on some properties of conditional expectation operators. We provide a necessary and sufficient condition for the *-multiplication operators to have closed range. Finally, a necessary condition for Fredholmness of these type of operators will be investigated.

scholarly journals Ulam Stability for a Class of Hill’s Equations

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1483 ◽  
Author(s):  
Ryuma Fukutaka ◽  
Masakazu Onitsuka
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Stability Constants ◽  
Sufficient Condition ◽  
Ulam Stability ◽  
Necessary And Sufficient Condition ◽  
Hill’S Equation ◽  
Hill’S Equations ◽  
Necessary And Sufficient ◽  
Ulam’S Type Stability

This paper deals with Ulam’s type stability for a class of Hill’s equations. In the two assertions of the main theorem, we obtain Ulam stability constants that are symmetrical to each other. By combining the obtained results, a necessary and sufficient condition for Ulam stability of a Hill’s equation is established. The results are generalized to nonhomogeneous Hill’s equations, and then application examples are presented. In particular, it is shown that if the approximate solution is unbounded, then there is an unbounded exact solution.

Two-weight weak and extra-weak type inequalities for the one-sided maximal operator

1993 ◽  
Vol 123 (6) ◽  
pp. 1109-1118
Author(s):  
Pedro Ortega Salvador ◽  
Luboš Pick
Keyword(s):  
Maximal Operator ◽  
Weak Type ◽  
Orlicz Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weight Functions ◽  
The One ◽  
Image Position ◽  
Necessary And Sufficient

SynopsisLet be the one-sided maximal operator and let Ф be a convex non-decreasing function on (0, ∞), Ф(0) = 0. We present necessary and sufficient conditions on a couple of weight functions (σ, ϱ) such that the integral inqualities of weak typeand of extra-weak typehold. Our proofs do not refer to the theory of Orlicz spaces.

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.

scholarly journals Exact Solution of a Linear Difference Equation in a Finite Number of Steps

2018 ◽  
Vol 14 (1) ◽  
pp. 7560-7563
Author(s):  
Sergey Mikhailovich Skovpen ◽  
Albert Saitovich Iskhakov
Keyword(s):  
Exact Solution ◽  
Difference Equation ◽  
Finite Number ◽  
Algebraic System ◽  
Linear Difference Equation ◽  
Algebraic Equations ◽  
Necessary And Sufficient Condition ◽  
Linear Algebraic Equations ◽  
Iterative Equations ◽  
Necessary And Sufficient

An exact solution of a linear difference equation in a finite number of steps has been obtained. This refutes the conventional wisdom that a simple iterative method for solving a system of linear algebraic equations is approximate. The nilpotency of the iteration matrix is the necessary and sufficient condition for getting an exact solution. The examples of iterative equations providing an exact solution to the simplest algebraic system are presented.

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