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- Title
MATRIX TRANSFORMS OF THE SET OF α-ABSOLUTELY CONVERGENT SEQUENCES WITH SPEED.
- Authors
Aasma, Ants; Natarajan, Pinnangudi Narayanasubramanian
- Abstract
We define the notion of α-absolute convergence with speed, where the speed is defined by a monotonically increasing positive sequence λ and 0 < α ≤ 1. Also we present the notion of α-absolute λ-conservativity of a matrix, and the notion of improvement of α-absolute λ-convergence by a matrix. Let lαλbe the set of all α-absolutely λ-convergent sequences and Y a sequence space defined by another speed µ. In this paper, we give necessary and sufficient conditions for a matrix A (with real or complex entries) to map lαλ into Y. We also present some examples of matrices being α-absolutely λ-conservative or improving the α-absolute λ-convergence, and consider these problems in the special cases if A is the Riesz matrix (R, pn) or the Zweier matrix Z1/2.
- Subjects
SEQUENCE spaces; SPEED
- Publication
Serdica Mathematical Journal, 2024, Vol 50, Issue 2, p137
- ISSN
1310-6600
- Publication type
Article
- DOI
10.55630/serdica.2024.50.137-150