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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
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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

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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