Sublinear function

In linear algebra and related areas of mathematics a function on a vector space V over the field F (which is either the real numbers R or the complex numbers C) is called sublinear if for all scalars γ and vectors x and y

$f(\gamma x) = \vert \gamma \vert f(x)$ (positive homogenity)

$f(x + y) \le f(x) + f(y)$ (subadditivity)

Examples

Every (semi-)norm is a sublinear function

Properties

Every sublinear function is a convex function

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See also: Sublinear function, Complex numbers, Convex function, Linear algebra, Mathematics, Norm (mathematics), Real numbers, Scalar, Subadditive function