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Summability methods which include the Riesz typical means. II

Published online by Cambridge University Press:  24 October 2008

B. C. Russell
B. C. Russell
Affiliation:
York University, Toronto
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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

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References

REFERENCES

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