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Convergence and summability factors in a sequence (II)

Part of: Direct theorems on summability

Published online by Cambridge University Press:  26 February 2010

L. S. Bosanquet
L. S. Bosanquet
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E 6BT
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Extract

1.1. In an earlier paper [6] the author proved

Theorem A. If α ≥ 0, β ≥ 0 (α, β integers), p > –1, p–r > –1 then necessary and sufficient conditions for a sequence (εn) to be such that

are

and

If α ≥ 1 (α an integer) and (ii) holds, then (i)bis equivalent to

MSC classification

Secondary: 40D15: Convergence factors and summability factors
Type
Research Article
Information
Mathematika , Volume 30 , Issue 2 , December 1983 , pp. 255 - 273
Copyright
Copyright © University College London 1983

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