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Extension of a theorem of Sunouchi

Published online by Cambridge University Press:  24 October 2008

V. P. Srivastava
V. P. Srivastava
Affiliation:
University of Delhi
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1·1. Definitions and notations. Let ∑an be a given infinite series, and let sn be its nth partial sum. We denote by and the nth Cesàro means of order α(α > − 1) of the sequences {sn} and {n. an} respectively.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 2 , March 1969 , pp. 489 - 494
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Bosanquet, L. S.Note on the Bohr–Hardy theorem. J. London Math. Soc. 17 (1942), 166–173.CrossRefGoogle Scholar
(2)Bosanquet, L. S.Note on convergence and summability factors. J. London Math. Soc. 20 (1945), 39–48.CrossRefGoogle Scholar
(3)Cheng, M. T.Summability factors of Fourier series. Duke Math. J. 15 (1948), 17–27.Google Scholar
(4)Chow, H. C.Note on convergence and summability factors. J. London Math. Soc. 29 (1954), 459–476.CrossRefGoogle Scholar
(5)Dikshit, G. D.On the absolute summability factors of infinite series. Proc. Nat. Inst. Sci. India Part A 25, 3 (1959), 191–200.Google Scholar
(6)Fekete, M.Zur theorie der divergenten Reihen. Mathematikai és termeszettudomanyi Értesitö (Budapest). 29 (1911), 719–726.Google Scholar
(7)Hardy, G. H.Divergent series (Oxford, 1949).Google Scholar
(8)Kogbetliantz, E.Sur les séries absolument sommable par la methode des moyennes arithmétiques. Bull. Sci. Math. (2), 49 (1925), 234–256.Google Scholar
(9)Kogbetliantz, E.Sommation des séries et intégrates divergentes par les moyennes arithmétiques et typiques. Mémor. Sci. Math. 51 (1931).Google Scholar
(10)Peyerimhoff, A.Summability factors for absolute Cesàro summable series. Math. Z. 59 (1954), 417–424.CrossRefGoogle Scholar
(11)Prasad, B. N. and Bhatt, S. N.The summability factors of a Fourier series. Duke Math. J. 24 (1957), 103–117.CrossRefGoogle Scholar
(12)Sunouchi, G.On the absolute summability factors. Kōdai Mathematical Seminar Report, 1954.CrossRefGoogle Scholar