Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-17T10:07:45.563Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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