AoPSWiki

Visit the AoPS Book Store.

Personal tools

Log in

Search

Toolbox

Karamata's Inequality

From AoPSWiki

Karamata's Inequality states that if $(x_i)$ majores $(y_i)$ and $f$ is a convex function, then

$\sum_{i=1}^{n}f(x_i)\geq \sum_{i=1}^{n}f(y_i)$

Proof

This proof is incomplete. You can help us out by completing it.

See also

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/Karamata%27s_Inequality"

Categories: Incomplete material | Theorems | Inequality

Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.

© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us