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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

A comparison between Euler and Cesàro methods of summability


Authors: B. Kuttner and M. R. Parameswaran
Journal: Proc. Amer. Math. Soc. 122 (1994), 787-790
MSC: Primary 40D20; Secondary 40G05
MathSciNet review: 1205495
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Abstract: It is well known that there are sequences that are summable by every Cesàro method $ {C_r}\;(r > 0)$ but are not summable by any Euler method $ {E_p}\;(0 < p < 1)$. It is proved here that on the other hand there are sequences that are summable by every Euler method $ {E_p}\;(0 < p < 1)$ but are not summable by any Cesaro method.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1205495-9
PII: S 0002-9939(1994)1205495-9
Article copyright: © Copyright 1994 American Mathematical Society