A subadditive function is a function $f : A \rightarrow B$ with the following property : $$ \forall x, y \in A,~~~~~f(x+y) \leq f(x) + f(y),$$ where both $A$ and $B$ are closed under addition.
I'm wondering if there is a name for the following closely related property : $$ \exists M > 0, \forall x, y \in A,~~~~~ f(x+y) \leq M\Big(f(x) + f(y)\Big).$$