Summability methods which include the Riesz typical means. II
Published online by Cambridge University Press: 24 October 2008
Extract
By making use of a convergence-factor theorem of Bosanquet(3), Cooke((4), Theorem I) gave conditions for a regular sequence-to-sequence summability matrix B to be at least as strong as Cesàro summability (C, κ) (κ > 0), namely:
Theorem C. Let κ > 0. In order that the T-matrix B = (bρμ) shall satisfy B ⊇ (C, κ) it is necessary and sufficient that
If 0 < κ ≤ 1 then (2) alone is necessary and sufficient.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 2 , March 1971 , pp. 297 - 300
- Copyright
- Copyright © Cambridge Philosophical Society 1971
References
REFERENCES
- 3
- Cited by