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.
Robert A. Adams and John J. F. Foutnier, Sobolev Space (2nd Edition, 2003), p54 ↩︎