The validity of Shapiro's cyclic inequality
Author:
B. A. Troesch
Journal:
Math. Comp. 53 (1989), 657664
MSC:
Primary 26D15
MathSciNet review:
983563
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Abstract: A cyclic sum is formed with N components of a vector x, where in the sum , , and where all denominators are positive and all numerators are nonnegative. It is known that there exist vectors x for which if and even, and if . It has been proved that the inequality holds for . Although it has been conjectured repeatedly that the inequality also holds for odd N between 15 and 23, this has apparently never been proved. Here we will confirm that the inequality indeed holds for all odd . This settles the question for all N.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198909835630
PII:
S 00255718(1989)09835630
Keywords:
Cyclic inequality,
cyclic sum,
minimization
Article copyright:
© Copyright 1989
American Mathematical Society
