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On the absolute Cesaro summability factors of trigonometric series

Published online by Cambridge University Press:  20 January 2009

Niranjan Singh
Affiliation:
Department of Mathematics and Statistics, Aligarh Muslim University, Aligarh (UP), India.
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Let be any given infinite series with sn as its n-th partial sum.

We write

and

where

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1968

References

REFERENCES

(1) Kogbetliantz, E., Sur les sśries absolument sommables per la méthodes des moyennes, Bulletin de Sciences Mathematiques, (2), 49 (1925), 234256.Google Scholar
(2) Pati, T., The absolute summability factors of infinite series, Duke Math. Journal 21 (1954), 271283.CrossRefGoogle Scholar
(3) Rajchman, A. and Saks, S., Sur la derivabilité des fonctions monotones, Fundamenta Mathematicae, 4 (1923), 204213.CrossRefGoogle Scholar
(4) Wang, F. T., Note on the absolute summability of Fourier series, J. London Math. Soc. 16 (1941), 174176.CrossRefGoogle Scholar
(5) Wang, F. T., The absolute Cesaro-summability of trigonometric series, Duke Math. Journal 9 (1942), 567572.CrossRefGoogle Scholar
(6) Ulyanov, P. L., Solved and unsolved problems in the theory of trigonometric and orthogonal series, Russian Math. Surveys, 19 (1964), 162.CrossRefGoogle Scholar