Superlinear functional ($q(x+y)\ge q(x)+q(y),q(tx)=tq(x)(t\ge 0)$)

In the functional-analytic sense used here, a superlinear functional is real valued, positively homogeneous and superadditive. Equivalently $-q$ is a sublinear functional. This definition concerns functional inequalities, rather than a comparison of asymptotic growth rates. Such a $q$ is concave, satisfies $q(0)=0$, and can serve as a lower support in the sandwich form of the Hahn-Banach theorem.