Wyniki wyszukiwania - BazTech

1

Normal structure in modulated topological vector spaces

Kozlowski Wojciech M.

Commentationes Mathematicae

|

2020

|

Vol. 60, No. 1/2

1--11

EN

Following the author’s recent paper On modulated topological vector spaces and applications, Bull. Aust. Math. Soc. (2020), we discuss a notion of modulated topological vector spaces, that generalise, among others, Banach spaces and modular function spaces. The interest in modulars reflects the fact that the notions of “norm like” but “non-euclidean” (i.e., possibly without the triangle property and non-necessarily homogenous) constructs to measure a level of proximity between complex objects have been used extensively in statistics and applied in many empirical scientific projects requiring an objective differentiation between several classes of objects, efficiently applied in many modern clustering and Artificial Intelligence (AI) related computer algorithms. As an example of application, we prove some results, which extend fixed point theorems from the above mentioned paper, by moving from the setting of admissible sets to a simpler and more general setup, which covers also closed bounded sets. The theory of modulated topological vector spaces provides a very minimalistic framework, where powerful geometrical, fixed point, approximation and optimisation theorems are valid under a bare minimum of assumptions.

2

On the Lebesgue and Sobolev spaces on a time-scale

Skrzypek Ewa, Szymańska-Dębowska Katarzyna

Opuscula Mathematica

|

2019

|

Vol. 39, no. 5

705--731

EN

We consider the generalized Lebesgue and Sobolev spaces on a bounded time-scale. We study the standard properties of these spaces and compare them to the classical known results for the Lebesgue and Sobolev spaces on a bounded interval. These results provide the necessary framework for the study of boundary value problems on bounded time-scales.

3

On spaces with mixed modulars and some spaces of temperate distributions

Musielak J.

Control and Cybernetics

|

2007

|

Vol. 36, no 3

833-839

EN

Extending the Benedek-Panzone spaces of functions iritegrable with mixed powers in R2, the spaces are investigated of functions integrable with mixed Orlicz functions, with application to Besov-type spaces and Triebel-Lisorkin spaces of temperate distributions.

4

Some remarks on strong convergence in modular spaces of sequences

Waszak A.

Fasciculi Mathematici

|

2005

|

Nr 35

151-162

EN

In this paper we study some connections between strong (A,φ)-summability of sequences and lacunary statistical convergence or lacunary strong convergence with respect to a modulus functions.

5

A contribution to the theory of modular spaces of sequences

Waszak A.

Fasciculi Mathematici

|

2004

|

Nr 34

149-156

EN

For a given space T of all real sequences, non-negative matrix A = (a(nm)) and two sequences of convex Phi - functions (Phi p = ((Phim) and Psi = (Psi/m) we considered two modular spaces of sequences T Phi, and T*GgPsi. This note contains theorems which determinate relationship betveen these spaces.

6

On the strong convergence in some sequence spaces

Waszak A.

Fasciculi Mathematici

|

2002

|

Nr 33

125-137

EN

The purpose of this paper is to introduce and study an idea of lacunary strong (A,phi)-convergence with respect to a modulus function. In coures of these investigations we study some connections between (A, phi)-strong summability of sequences and lacunary strong convergence with respect to a modulus or lacunary statistical convergence.

7

On properties of some modular spaces of double sequences

Waszak A.

Fasciculi Mathematici

|

2001

|

Nr 32

105-116

EN

We consider modular spaces of strong (A, fi) - summable and | A,fi -summable double sequences. The main results are two theorems in which are given the necessary conditions for inclusion between the spaces T(fi) and 7(fi). These theorems are generalization of theorems given by J. Musielak and W. Orlicz in [6].