Sublinear Functional

In the setting of Separable Real Normed Spaces and Hahn–Banach: Notation, let $V$ be a real vector space and let $p:V\to\mathbb{R}$ be a function.

(i) Subadditivity. $p(x+y)\le p(x)+p(y)$ for all $x,y\in V$.

(ii) Nonnegative homogeneity. $p(\lambda x)=\lambda\,p(x)$ for all $x\in V$ and every real $\lambda\ge0$.

(iii) Sublinear functional. $p$ is a sublinear functional on $V$ if it satisfies (i) and (ii).