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On the relation between the Abel-type and Borel-type methods of summability

Authors: B. L. R. Shawyer and G. S. Yang
Journal: Proc. Amer. Math. Soc. 26 (1970), 323-328
MSC: Primary 40.33
MathSciNet review: 0264276
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Abstract: In recent papers, R. Jajte and B. L. R. Shawyer have proved that under certain conditions a series summable by a Borel-type or absolute Borel-type method of summability is also summable by the Abel or absolute Abel method of summability to the same sum. In the present paper, the Abel method is replaced by the more general Abel-type method, giving similar results for ordinary, strong and absolute summability.

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Keywords: Ordinary, strong, absolute, Abel-type summability methods, Borel-type summability methods
Article copyright: © Copyright 1970 American Mathematical Society

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