Schur-convex function: Difference between revisions

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Revision as of 13:55, 1 August 2011

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In mathematics, a '''Schur-convex function''', also known as '''S-convex''', '''isotonic function''' and '''order-preserving function''' is a [[function (mathematics)|function]] <math>f: \mathbb{R}^d\rightarrow \mathbb{R}</math>, for which if <math>\forall x,y\in \mathbb{R}^d </math> where <math>x</math> is [[majorization|majorized]] by <math>y</math>, then <math>f(x)\le f(y)</math>. Named after [[Issai Schur]], Schur-convex functions are used in the study of [[majorization]]. Every function that is [[Convex function|convex]] and [[Symmetric_functionSymmetric function|symmetric]] is also Schur-convex.

== Schur-concave function ==

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* <math>\sum_{i=1}^d{x_i^k},k \ge 1</math> is Schur-convex

[[categoryCategory:convexConvex analysis]]

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[[Category:Inequalities]]

[[category:convex analysis]]

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