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Absolute Summability Factors in a Sequence

Published online by Cambridge University Press:  20 November 2018

S. Baron
S. Baron*
Affiliation:
Department of Mathematics and Computer Science Bar Ilan University 52 100 Ramat Gan, Israel
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Abstract

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Let α≥0 and β>— 1. The main result gives necessary and sufficient conditions for the sequence (εn) in order that the sequence (εnUn) will be absolutely summable by the Cesàro method Cβ for each sequence (Un) which is bounded or summable by the method Cα

Another theorem is proven when Cα and Cβ are replaced by triangular methods A = (ank) and B=(bnk) satisfying , where (ξnk) = (ank)-1.

Keywords

40D1540 G 05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 1 , 01 March 1984 , pp. 16 - 30
Copyright
Copyright © Canadian Mathematical Society 1984

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