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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 (εn U n) 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

Information

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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