We consider a power series $g \in O_1$ with non-negative real coefficients. We assume that there exist $a > 0, b > 0$ such that
$$g \prec a\left(I + \frac{g^2}{b - g}\right)$$
and $h$ is the function from question (11). Show, by induction on $k$, that $(g)_k \leqslant (h)_k$ for all $k \in \mathbb{N}$, conclude.