Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-23T00:57:20.059Z Has data issue: false hasContentIssue false
  • English
  • Français

Summability Methods Definedby Riemann Sums

Published online by Cambridge University Press:  20 November 2018

J. D. Hill
J. D. Hill*
Affiliation:
Michigan State College
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.

Let f(x) be real valued, bounded and, integrable in the sense of Riemann on the interval X = (0 < x < 1), with the value of its integral over X equal to one. For brevity we call such a function admissible.The symbol Xnk will always denote the interval an arbitrarily chosen point of Xnk and δ any specified set of intermediate points

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 289 - 296
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Agnew, R. P., On equivalence of methods of evaluation of sequences, Tôhoku Math., J., 35 (1932), 244–252.Google Scholar
2. Carr, R. E. and Hill, J. D., Pattern integration, Proc. Amer. Math. Soc, 2 (1951), 242–245.Google Scholar
3. Cooke, R. G., Infinite matrices and sequence spaces (London, 1950).Google Scholar
4. Kogbetliantz, E., Sommation des series et intégrales divergentes par les moyennes arithmétiques et typiques (Paris, 1931).Google Scholar
5. Rado, R., Some elementary Tauberian theorems I, Quarterly J. Math., 9 (1938), 274–282.Google Scholar
6. Riesz, M., Sur l'équivalence de certaines méthodes de sommation, Proc. London Math. Soc. (2), 22 (1923), 412–419.Google Scholar
7. Woronoi, G. F. and Tamarkin, J. D., Extensions of the notion of the limit of the sum of the terms of an infinite series, Ann. Math. (2), 33 (1932), 422–428.Google Scholar