Shapiro inequality

Let n be a positive integer and let x1,,xn be positive reals. If n is even and n12, or n is odd and n23, then


where the subscripts are to be understood modulo n.

The particular case of n=3 is also known as Nesbitts inequality.

Title Shapiro inequality
Canonical name ShapiroInequality
Date of creation 2013-03-22 13:43:15
Last modified on 2013-03-22 13:43:15
Owner Koro (127)
Last modified by Koro (127)
Numerical id 7
Author Koro (127)
Entry type Theorem
Classification msc 26D05
Synonym Shapiro’s inequalityMathworldPlanetmath
Related topic NesbittsInequality