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Generalized Nörlund means and consistency theorems

Published online by Cambridge University Press:  24 October 2008

I. J. Maddox
I. J. Maddox
Affiliation:
Queen's University of Belfast
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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

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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