Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-29T18:59:49.030Z Has data issue: false hasContentIssue false
  • English
  • Français

On some inequalities of H. Kober

Published online by Cambridge University Press:  24 October 2008

P. H. Diananda
P. H. Diananda
Affiliation:
Department of Mathematics, University of Singapore
Get access Rights & Permissions [Opens in a new window]

Extract

Throughout this paper q1,q2,… are positive and x1,x2,… non-negative real numbers. When q1+…+ qn = 1, we define Δn, Sn and Σn as follows:

and

We use the term ‘comparable’ in Kober's(2) sense. Two functions f(x1, …, xn) and g(x1, …, xn) are comparable if and only if αg ≤ f ≤ βg for some positive constants α and β.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 341 - 346
Copyright
Copyright © Cambridge Philosophical Society 1963

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

REFERENCES

(1)Diananda, P. H., On a conjecture of L. J. Mordell regarding an inequality involving quadratic forms. J. London Math. Soc. 36 (1961), 185–192.Google Scholar
(2)Kober, H., On the arithmetic and geometric means and on Hölder's inequality. Proc. American Math. Soc. 9 (1958), 452–459.Google Scholar