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Some Cyclic and Other Inequalities

Published online by Cambridge University Press:  24 October 2008

P. H. Diananda
P. H. Diananda
Affiliation:
Department or Mathematics University of Malaya in Singapore*
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Extract

In a recent paper (2) Rankin has proved that for all positive integral n where As stated by Rankin, his proof is not simple although it is based on elementary ideas. Also, as noted by him, no other proof is available for any inequality of the form with λ a positive constant independent of n. It is the main purpose of this note to give a simple proof for the following result which implies the truth of (3) with λ = ¼, though not the truth of (1).

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 2 , April 1962 , pp. 425 - 427
Copyright
Copyright © Cambridge Philosophical Society 1962

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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.CrossRefGoogle Scholar
(2)Rankin, R. A.A cyclic inequality. Proc. Edinburgh Math. Soc. 12 (1961), 139–147.CrossRefGoogle Scholar