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Generalized Nörlund means and consistency theorems
Published online by Cambridge University Press: 24 October 2008
Extract
It was recently shown in (1), corollary 1, that if (I) = (N, q) then I and (N, q) were consistent. By I we denote the unit infinite matrix, and (N, q) denotes a general complex Nörlund mean. The summability field (A) of any infinite matrix A = (ank) is defined as
where c is the space of convergent sequences. The summability field of (N, q) is, for simplicity, written as (N, q) instead of ((N, q)).
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 2 , March 1980 , pp. 243 - 248
- Copyright
- Copyright © Cambridge Philosophical Society 1980
References
REFERENCES
(1)Maddox, I. J.Consistency and Nörlund means. Math. Proc. Cambridge Philos. Soc. 82 (1977), 107–109.CrossRefGoogle Scholar
(2)Robinson, A.On functional transformations and summability. Proc. London Math. Soc. (2), 52 (1950), 132–160.CrossRefGoogle Scholar