Karamata's Inequality: Difference between revisions

Revision as of 20:40, 2 June 2012

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

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

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	'''Karamata's Inequality''' states that if <math>(x_i)</math> [[Majorization\|~~majores~~]] <math>(y_i)</math> and <math>f</math> is a [[convex function]], then		'''Karamata's Inequality''' states that if <math>(x_i)</math> [[Majorization\|majorizes]] <math>(y_i)</math> and <math>f</math> is a [[convex function]], then

	<center><math>\sum_{i=1}^{n}f(x_i)\geq \sum_{i=1}^{n}f(y_i)</math></center>		<center><math>\sum_{i=1}^{n}f(x_i)\geq \sum_{i=1}^{n}f(y_i)</math></center>