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Karamata's Inequality

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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

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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.

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