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On generalized Nörlund methods of summability II

Published online by Cambridge University Press:  17 April 2009

Minoru Tanaka
Minoru Tanaka
Affiliation:
Department of Mathematics, Faculty of Sciences, Chiba University, Chiba 280, Japan.
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Abstract

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The object of this paper is to establish some inclusion relations between two generalized Nörlund methods of summability. Our results are generalizations of Das's Theorem and one of them is also a generalization of a theorem of the author. They include the well-known fact that the Cesàro method (C, α) is weaker than (C, β) for β > α > 0.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 22 , Issue 2 , October 1980 , pp. 231 - 239
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Das, G., “On some methods of summability (II)”, Quart. J. Math. Oxford Ser. 19 (1968), 417–431.CrossRefGoogle Scholar
[2]Hardy, G.H., Divergent series (Clarendon Press, Oxford, 1949).Google Scholar
[3]Kishore, Nand, “Inclusion and equivalence of absolute Nörlund summability methods”, Indian J. Math. 12 (1970), 1–12.Google Scholar
[4]Tanaka, Minoru, “On generalized Nörlund methods of summability”, Bull. Austral. Math. Soc. 19 (1978), 381–402.CrossRefGoogle Scholar