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In this paper we define new sequence spaces using the concepts of strong summability and boundedness of index $p > 0$ of $r$ -th order difference sequences. We establish sufficient conditions for these spaces to reduce to certain spaces of null and bounded sequences.

Bases in Sequence Spaces and Expansion of a Function in a Series of Power Series

Bruno de Malafosse — 2000

Matematički Vesnik

Some new Properties of Sequence Spaces and Application to the Continued Fractions

Bruno de Malafosse — 2001

Matematički Vesnik

Application of the infinite matrix theory to the solvability of certain sequence spaces equations with operators

Bruno de Malafosse — 2012

Matematički Vesnik

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Variation of an element in the matrix of the first difference operator and matrix transformations.

The Banach algebra $B (X$ ), where $X$ is a BK space and applications.

Some properties of the sum of linear operators in the non-differential case.

Calculations on some sequence spaces.

On the Banach algebra $ℬ (l_{p} (α))$ .

On the sets of sequences that are strongly $α$ -bounded and $α$ -convergent to naught with index $p$ .

On some BK spaces.

Matrix transformations and generators of analytic semigroups.

Measure of noncompactness of operators and matrices on the spaces $c$ and $c_{0}$ .

Matrix transformations and quasi-Newton methods.

The space $S_{α, β}$ and σ-core

Calculations in new sequence spaces

Bases in Sequence Spaces and Expansion of a Function in a Series of Power Series

Some new Properties of Sequence Spaces and Application to the Continued Fractions

Application of the infinite matrix theory to the solvability of certain sequence spaces equations with operators