= Superlinear functional
{title2=$q(x+y)\geq q(x)+q(y),\quad q(tx)=tq(x)\ (t\geq0)$}
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>.
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