Schur-convex function: Difference between revisions

Revision as of 05:56, 30 September 2007

Revision as of 23:52, 12 March 2008

Line 1:

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_functionConvex function|convex]] and [[Symmetric_function|symmetric]] is also Schur-convex.

== Schur-concave function ==

A function <math>f</math> is '''Schur-concave''' if <math>-f</math> is Schur-convex.

== Examples ==