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Function which have Generalized Riemann Derivatives

Published online by Cambridge University Press:  20 November 2018

C. Kassimatis
C. Kassimatis*
Affiliation:
Queen's University
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Letƒ(x) be a measurable function denned in the interval (a, b), and let If the limit of exists and is finite at the point x, as h → 0, it is called the wth generalized Riemann derivative of ƒ(x) at the point x, Dnƒ(x).

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958, pp. 413 - 420
Copyright
Copyright © Canadian Mathematical Society 1958 

Footnotes

The author wishes to express his appreciation to Professor R. L. Jeffery for suggesting this investigation.

References

1. Corominas, E., Contribution à la théorie de la dérivation d'ordre supérieur, Bull. Soc. Math. France, (part 3) 81 (1953), 177-222.Google Scholar
2. Denjoy, A., Leçons sur le calcul des coefficients d'une série trigonométrique (Paris, 1941 and 1949).Google Scholar
3.James, R. D., A generalized integral II, Can. J. Math., 2 (1950), 297-306.Google Scholar
4. Jeffery, R. L., Trigonometric series (Toronto, 1956).Google Scholar
5. Marcinkiewicz, J. and Zygmund, A., On the differentiability of functions and summability of trigonometrical series, Fund. Math., 26 (1936), 1-43.Google Scholar
6. Verblunsky, S., The generalized third derivative and its application to the theory of trigonometric series, Proc. Lond. Math. Soc. (2), 31 (1930), 387-406.Google Scholar