- Dettagli della rivista
- Formato
- Rivista
- eISSN
- 1338-9750
- Pubblicato per la prima volta
- 12 Nov 2012
- Periodo di pubblicazione
- 3 volte all'anno
- Lingue
- Inglese

#### Cerca

- Accesso libero

The Family of Central Cantor Sets with Packing Dimension Zero

Pagine: 1 - 8

#### Astratto

As in the recent article of M. Balcerzak, T. Filipczak and P. Nowakowski, we identify the family ^{ℕ} equipped with the probability product measure _{0} of sets in _{0} is meager and of _{0} and other subfamilies

#### Parole chiave

- central Cantor sets
- Baire category
- product measure
- sets of packing dimension zero

#### Astratto

In 2014, J. Borsík and J. Holos defined porouscontinuous functions. Using the notion of density in O’Malley sense, we introduce new definitions of porouscontinuity, namely _{r}_{r}

#### Parole chiave

- porosity
- porouscontinuity
- porouscontinuity in O’Malley sense

- Accesso libero

Generalized Densities on ℝ^{n} and their Applications

^{n}and their Applications

Pagine: 25 - 42

#### Astratto

We examine some generalized densities (called (

#### Parole chiave

- - density point
- - density topology
- similarity of topologies
- differentiation basis
- base operator
- set of finite perimeter
- Sobolev space

- Accesso libero

Local Properties of Entropy for Finite Family of Functions

Pagine: 43 - 58

#### Astratto

In this paper we consider the issues of local entropy for a finite family of generators (that generates the semigroup). Our main aim is to show that any continuous function can be approximated by s-chaotic family of generators.

#### Parole chiave

- entropy
- semigroup
- set of generators
- entropy of I, II, III type
- (periodic) dynamical system
- -invariant set
- -entropy point ( ∈ {I, II, III})
- s-chaotic set of generators

- Accesso libero

A Fixed Point Approach to the Hyers-Ulam-Rassias Stability Problem of Pexiderized Functional Equation in Modular Spaces

Pagine: 59 - 72

#### Astratto

In this paper, we consider pexiderized functional equations for studying their Hyers-Ulam-Rassias stability. This stability has been studied for a variety of mathematical structures. Our framework of discussion is a modular space. We adopt a fixed-point approach to the problem in which we use a generalized contraction mapping principle in modular spaces. The result is illustrated with an example.

#### Parole chiave

- Hyers-Ulam-Rassias stability
- pexiderized functional equation
- modular spaces
- fixed point method

- Accesso libero

A Certain Subclass of Analytic Functions with Negative Coefficients Defined by Gegenbauer Polynomials

Pagine: 73 - 84

#### Astratto

In this paper, we introduce a new subclass of analytic functions with negative coefficients defined by Gegenbauer polynomials. We obtain coefficient bounds, growth and distortion properties, extreme points and radii of starlikeness, convexity and close-to-convexity for functions belonging to the class

#### Parole chiave

- analytic
- coefficient bounds
- extreme points
- convolution
- polynomial

- Accesso libero

Super and Hyper Products of Super Relations

Pagine: 85 - 118

#### Astratto

If

Motivated by an ingenious idea of Emilia Przemska on a unified treatment of open- and closed-like sets, we shall introduce and investigate here four reasonable notions of product relations for super relations.

In particular, for any two super relations

By using the distributivity of the operation ∩ over ∪, we can at once see that ^{c}^{c}

#### Parole chiave

- relations on ordinary and power sets
- unary and binary operations for relations
- Galois connections
- generalized uniformities
- generalized open sets

- Accesso libero

Łukasiewicz Logic and the Divisible Extension of Probability Theory

Pagine: 119 - 128

#### Astratto

We show that measurable fuzzy sets carrying the multivalued Łukasiewicz logic lead to a natural generalization of the classical Kolmogorovian probability theory. The transition from Boolean logic to Łukasiewicz logic has a categorical background and the resulting divisible probability theory possesses both fuzzy and quantum qualities. Observables of the divisible probability theory play an analogous role as classical random variables: to convey stochastic information from one system to another one. Observables preserving the Łukasiewicz logic are called conservative and characterize the “classical core” of divisible probability theory. They send crisp random events to crisp random events and Dirac probability measures to Dirac probability measures. The nonconservative observables send some crisp random events to genuine fuzzy events and some Dirac probability measures to nondegenerated probability measures. They constitute the added value of transition from classical to divisible probability theory.

#### Parole chiave

- divisible extension of probability theory
- Boolean logic
- random variable
- observable
- statistical map
- stochastic channel
- Łukasiewicz logic
- full Łukasiewicz tribe
- conservative observable

- Accesso libero

Around Taylor’s Theorem on the Convergence of Sequences of Functions

Pagine: 129 - 138

#### Astratto

Egoroff’s classical theorem shows that from a pointwise convergence we can get a uniform convergence outside the set of an arbitrary small measure. Taylor’s theorem shows the possibility of controlling the convergence of the sequences of functions on the set of the full measure. Namely, for every sequence of real-valued measurable factions |_{n}_{n∈ℕ} pointwise converging to a function _{n}_{n∈ℕ} of positive reals converging to 0 and a set _{n}_{n∈ℕ}. The main results of the paper concern basic properties of sets of all such sequences for a given set

#### Parole chiave

- sequences of real-valued functions
- convergence

- Accesso libero

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

Pagine: 139 - 156

#### Astratto

We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group

#### Parole chiave

- vector lattice
- order bounded functional
- order continuous functional
- amenability
- Hahn-Banach theorem
- sandwich theorem
- Fenchel duality theorem
- subgradient
- subdifferential of composite functions
- optimality condition
- Moreau-Rockafellar formula
- Farkas theorem
- Kuhn-Tucker theorem

#### Astratto

A space X is said to have the star-K-_{n}_{n}_{n}, U_{n}

#### Parole chiave

- Hurewicz
- star-K--Hurewicz
- star-K-Hurewicz
- ideal
- covering
- star-covering
- topological space

- Accesso libero

Compactness of Multiplication Operators on Riesz Bounded Variation Spaces

Pagine: 167 - 174

#### Astratto

We prove compactness of the operator _{h}C_{g}_{h}_{g}

#### Parole chiave

- Riesz bounded variation
- multiplication operator
- compactness

- Accesso libero

On Functions Preserving Products of Certain Classes of Semimetric Spaces

Pagine: 175 - 198

#### Astratto

In the paper, we continue the research of Borsík and Doboš on functions which allow us to introduce a metric to the product of metric spaces. We extend their scope to a broader class of spaces which usually fail to satisfy the triangle inequality, albeit they tend to satisfy some weaker form of this axiom. In particular, we examine the behavior of functions preserving

#### Parole chiave

- semimetrics
- metric-preserving functions
- -metrics
- subadditive functions

#### Astratto

The paper tries to survey the recent results about relationships between covering properties of a topological space

#### Parole chiave

- cover
- upper semicontinuous function
- measurable function
- upper semimeasurable function
- bornology

#### Astratto

In this paper, we show there are strong relations between the algebraic properties of a graded commutative ring

#### Parole chiave

- graded prime ideal
- graded radical ideal
- Zariski topology