📂Functions

Semi-linear Function

Definition¹

If a function $f : X \to Y$ satisfies the following two conditions, it is called sublinear. For $x,x_{1},x_{2}\in X$ and $a \in \mathbb{R}$,

• $f(ax) = af(x)$
• $f(x_{1} + x_{2}) \le f(x_{1}) + f(x_{2})$

Explanation

If the second condition holds as an equality, it is linear, and if it holds as an inequality, it is sublinear.