The growth theorem of convex mappings on the unit ball in ${\mathbb{C}}^{n}$

Let $\Vert \cdot \Vert$ be an arbitrary norm on ${\mathbb{C}}^{n}$. Let $f$ be a normalized biholomorphic convex mapping on the unit ball in ${\mathbb{C}}^{n}$ with respect to the norm $\Vert \cdot \Vert$. We will give an upper bound of the growth of $f$.