In mathematics, a Schur-convex function, also known as S-convex, isotonic function and order-preserving function is a function ${\displaystyle f:\mathbb {R} ^{d}\rightarrow \mathbb {R} }$ that for all ${\displaystyle x,y\in \mathbb {R} ^{d}}$ such that ${\displaystyle x}$ is majorized by ${\displaystyle y}$, one has that ${\displaystyle f(x)\leq f(y)}$. Named after Issai Schur, Schur-convex functions are used in the study of majorization. Every function that is convex and symmetric is also Schur-convex. The opposite implication is not true, but all Schur-convex functions are symmetric (under permutations of the arguments).[1]