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On convergence and summability factors in a sequence

Published online by Cambridge University Press:  26 February 2010

L. S. Bosanquet
L. S. Bosanquet
Affiliation:
University College, London.
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Extract

The following theorem is typical of a group of results which have been found to be of importance in the theory of Cesàro summability.

Theorem A. If 0 ≤ ρ ≤ κ (κ, ρ integer), p > −1,p+q −1 and

and ifsn = 0(np) (C, κ), thensn εn = 0(np+q) (C, ρ).

Type
Research Article
Information
Mathematika , Volume 1 , Issue 1 , June 1954 , pp. 24 - 44
Copyright
Copyright © University College London 1954

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