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On the generalized Nakano sequence space

Sengonul M.

Demonstratio Mathematica

2007

Vol. 40, nr 4

885-893

The purpose of this note is to define and to investigate the generalized Nakano sequence space A(p) and to show that the sequence space A(p) eąuipped with the Luxemburg norm is rotund and posses property-H when p = (pk) is bounded with pk > 1 for all k is an element of N.

Some remarks on strong convergence in modular spaces of sequences

Waszak A.

Fasciculi Mathematici

2005

Nr 35

151-162

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.

A contribution to the theory of modular spaces of sequences

Waszak A.

Fasciculi Mathematici

2004

Nr 34

149-156

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.

On the strong convergence in some sequence spaces

Waszak A.

Fasciculi Mathematici

2002

Nr 33

125-137

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.

An application of modular spaces to approximation problems, IX

Stoiński S.

Fasciculi Mathematici

2002

Nr 33

89-97

By means of terms of a sequence (pn), where pn, n = l,2,..., are pseudomodulars, and by means of an infinite matrix A = [amn ] of non-negative numbers we shall construct the modular spaces XpAos' and Xp^os. Then we shall approximate elements of these spaces by means of terms of a sequence (p.), where p, i = l,2,..., are pseudomodulars. In particular, we will investigate the special cases when pn and pt are singular integrals.

An application of modular spaces to approximation problems, VII

Stoiński S.

Demonstratio Mathematica

2000

Vol. 33, nr 4

805-814

Approximation with respect to a measure in a modular space, VI

Stoiński S.

Fasciculi Mathematici

1999

Nr 29

125-131

Elements of a modular subspace of [...] are approximated by certain singular integrals.