Schur-convex function

In mathematics, a Schur-convex function, also known as S-convex, isotonic function and order-preserving function is a function $f:\mathbb {R} ^{d}\rightarrow \mathbb {R}$, for which if $\exists x,y\in \mathbb {R} ^{d}$ where $x$ is majorized by $y$, then $f(x)\leq f(y)$. Named after Issai Schur, Schur-convex functions are used in the study of majorization.

Schur-concave function

A function $f$ is Schur-concave if $-f$ is Schur-convex.

Examples

• Entropy