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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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