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Absolute total-effectiveness of (N, pn) means. I

Published online by Cambridge University Press:  24 October 2008

H. P. Dikshit  and
A. Kumar
H. P. Dikshit
Affiliation:
University of Jabalpur, India
A. Kumar
Affiliation:
University of Jabalpur, India
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Extract

1. Introduction. Using throughout the definitions and notations contained in (4), we state the following recent results by one of the present authors ((4), Theorem I and Theorem 2) which include as a special case the corresponding |C| – result due to Bosanquet (1), Bosanquet and Hyslop (2) and Hyslop(5).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 1 , January 1975 , pp. 103 - 108
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Bosanquet, L. S.The absolute Cesàro summability of a Fourier series. Proc. London Math. Soc. 41 (1936), 517–523.CrossRefGoogle Scholar
(2)Bosanquet, L. S. and Hyslop, J. M.On the absolute summability of the allied series of a Fourier series. Math. Z. 42 (1937), 487–512.CrossRefGoogle Scholar
(3)Dikshit, H. P.Absolute summability of a Fourier series by Nörlund means. Math. Z. 102 (1967), 166–170.Google Scholar
(4)Dikshit, H. P.Absolute total-effective (N, pn) means. Proc. Cambridge Philos, Soc. 69 (1971), 107–122.CrossRefGoogle Scholar
(5)Hyslop, J. M.On the absolute summability of the successively derived series of Fourier series and its allied series. Proc. London Math. Soc. 46 (1940), 55–80.CrossRefGoogle Scholar