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Vol. 50 No. 2 (2024)
Serdica Mathematical Journal

Articles

Matrix transforms of the set of α-absolutely convergent sequences with speed

https://doi.org/10.55630/serdica.2024.50.137-150

Published 13-08-2024

  • Ants Aasma
    • ,
  • P. N. Natarajan

Ants Aasma
Tallinn University of Technology

P. N. Natarajan
Ramakrishna Mission Vivekananda College

Abstract

We define the notion of \(\alpha\)-absolute convergence with speed, where the speed is defined by a monotonically increasing positive sequence \(\lambda\) and \(0< \alpha \leq 1\). Also we present the notion of \(\alpha\)-absolute \(\lambda\)-conservativity of a matrix, and the notion of improvement of \(\alpha\)-absolute \(\lambda\)-convergence by a matrix. Let \(l_{\alpha}^{\lambda}\) be the set of all \(\alpha\)-absolutely \(\lambda\)-convergent sequences and \(Y\) a sequence space defined by another speed \(\mu\). In this paper, we give necessary and sufficient conditions for a matrix \(A\) (with real or complex entries) to map \(l_{\alpha}^{\lambda}\) into \(Y\). We also present some examples of matrices being \(\alpha\)-absolutely \(\lambda\)-conservative or improving the \(\alpha\)-absolute \(\lambda\)-convergence, and consider these problems in the special cases if \(A\) is the Riesz matrix \((R,p_{n})\) or the Zweier matrix \(Z_{1/2}\).

2020 Mathematics Subject Classification:

40C05, 40D05, 41A25

Keywords

matrix transforms, boundedness, convergence and α-absolute convergence with speed, α-absolute λ-conservativity, improvement of α-absolute λ-convergence

Full text

Author Details

Ants Aasma

Tallinn University of Technology
Department of Economics and Finance
Akadeemia tee 3-456, 12618 Tallinn, Estonia
e-mail: ants.aasma@taltech.ee

P. N. Natarajan

Old No. 2/3, New No.3/3 Second Main Road
R. A. Puram, Chennai 600028 India
e-mail: pinnangudinatarajan@gmail.com

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