Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-24T23:42:42.914Z Has data issue: false hasContentIssue false

Function which have Generalized Riemann Derivatives

Published online by Cambridge University Press:  20 November 2018

C. Kassimatis*
Affiliation:
Queen's University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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).

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1958

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