Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-19T06:08:08.505Z Has data issue: false hasContentIssue false
  • English
  • Français

Integral mean value theorems and the Ganelius inequality

Published online by Cambridge University Press:  14 November 2011

Ian Knowles
Ian Knowles
Affiliation:
Department of Mathematics, University of Alabama in Birmingham, Birmingham, Alabama 35294, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

The inequality of Ganelius states that, for suitable functions f and g on an interval [a, b], [inf f + var f]sup ∫ jdg, where the supremum is taken over all sub-intervals J of [a, b]. A more general version of this inequality is derived as well as certain related generalized mean-value theorems.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 145 - 150
Copyright
Copyright © Royal Society of Edinburgh 1984

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

1Atkinson, F. V.. Limit-n criteria of integral type. Proc. Roy. Soc. Edinburgh Sect. A 73 (1975), 167–198.CrossRefGoogle Scholar
2Bonnet, P. O.. Mem. Acad. Belg. 23 (1850), 8.Google Scholar
3Brink, I.. Self-adjointness and spectra of Sturm-Liouville operators. Math. Scand. 7 (1959), 219–239.Google Scholar
4Reymond, P. D. G. Du Bois. Crelle's J. 69 (1869), 81.Google Scholar
5Evans, W. D.. On limit-point and Dirichlet-type results for second order differential expressions. Lecture Notes in Mathematics 564, 80–106 (Berlin: Springer, 1976). (Proceedings of the 1976 Dundee Conference on Differential Equations).Google Scholar
6Ganelius, T.. Un theoreme Tauberien pour la transformation de Laplace. C. R. Acad. Sci. Paris 242 (1956), 719–721.Google Scholar
7Ganelius, T.. An equality for Stieltjes integrals. Proc. of the 14th Scandinavian Mathematical Congress (Copenhagen, 1964).Google Scholar
8Hartman, P.. Ordinary Differential Equations (New York: Wiley, 1964).Google Scholar
9Hobson, E. W.. The Theory of Functions of a Real Variable. Vol. 1 (New York: Dover, 1957).Google Scholar
10Knowles, I.. A limit-point criterion for a second-order differential operator. J. London Math. Soc. 8 (1974), 719–728.Google Scholar
11Wüst, R.. Beweis eines Lemmas von Ganelius. Jahresber. Deutsch. Math.-Verein. 71 (1969), 229–230.Google Scholar