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)

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

Examples

• Every (semi-)norm is a sublinear function

Properties

• Every sublinear function is a convex function