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A Tauberian Theorem Concerning Borel-Type and Cesàro Methods of Summability

Published online by Cambridge University Press:  20 November 2018

David Borwein  and
Tom Markovich
David Borwein
Affiliation:
The University of Western Ontario, London, Ontario
Tom Markovich
Affiliation:
The University of Western Ontario, London, Ontario
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Suppose throughout that r ≧ 0, α > 0, αq + β > 0 where q is a non-negative integer. Let {sn} be a sequence of real numbers,

The Borel-type summability method (B, α, β) is defined as follows:

The method (B, α, β) is regular [5]; and (B, 1, 1) is the standard Borel exponential method B. For a real sequence {sn} we consider the slowly decreasing-type Tauberian condition

We shall also be concerned with the Cesàro summability method Cp(p > —1), the Valiron method Vα, and the Meyer-König method Sa (0 < a < 1) defined as follows:

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 1 , 01 February 1988 , pp. 228 - 247
Copyright
Copyright © Canadian Mathematical Society 1988

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