Schur-convex function

Named after Issai Schur, Schur-convex functions are used in the study of majorization.

A function f is 'Schur-concave' if its negative, −f, is Schur-convex.

Every function that is convex and symmetric (under permutations of the arguments) is also Schur-convex.

Every Schur-convex function is symmetric, but not necessarily convex.

is (strictly) Schur-convex and

is (strictly) monotonically increasing, then

is a convex function defined on a real interval, then

If f is symmetric and all first partial derivatives exist, then f is Schur-convex if and only if holds for all

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