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26.—On Shapiro's Cyclic Inequality

Published online by Cambridge University Press:  14 February 2012

P. J. Bushell  and
A. H. Craven
P. J. Bushell
Affiliation:
Mathematics Division, University of Sussex
A. H. Craven
Affiliation:
Mathematics Division, University of Sussex
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Synopsis

The inequality, for suitable sets of non-negative numbers x1, x2, …, xn,

is undecided in the cases n = 11, 12, 13, 15, 17, 19, 21 and 23. In this note we present the results of numerical analysis supporting the conjecture that the inequality is valid in these cases. A new counter–example for n = 25 and a new elementary proof when n = 7 are given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 75 , Issue 4 , 1976 , pp. 333 - 338
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

1Daykin, D. E.. Inequalities of a cyclic nature. J. London Math. Soc. 3 (1971), 453–462.CrossRefGoogle Scholar
2Diananda, P. H.. On a cyclic sum. Proc. Glasgow Math. Assoc. 6 (1963), 11–13.CrossRefGoogle Scholar
3Djokovic, D. Z.. Sur une inegalite. Proc. Glasgow Math. Assoc. 6 (1963), 1–10.CrossRefGoogle Scholar
4Malcolm, M. A.. A note on a conjecture of L. J. Mordell. Math. Comp. 25 (1971), 375–377.CrossRefGoogle Scholar
5Mitrinovic, D. S.. Analytic Inequalities (Berlin: Springer, 1970).CrossRefGoogle Scholar
6Mordell, L. J.. Note on the inequality . J. London Math. Soc. 37 (1962), 177–178.Google Scholar
7Nowosad, P.. Isoperimetric eigenvalue problems in algebras. Comm. Pure Appl. Math. 21 (1968), 401–465.CrossRefGoogle Scholar
8Zulauf, A.. Note on a conjecture of L. J. Mordell. Abh. Math. Sent. Univ. Hamburg 22 (1958), 229–240.Google Scholar