Formal solutions of the generalized Dhombres functional equation with value one at zero

We study formal solutions f of the generalized Dhombres functional equation ${f(zf(z)) = \varphi(f(z))}$ . Unlike in the situation where f(0) =?w ₀ and ${w_0 \in \mathbb{C}{\setminus} \mathbb{E}}$ where ${\mathbb{E}}$ denotes the complex roots of 1, which were already discussed, we investigate solutions f where f(0)?=?1. To obtain solutions in this case we use new methods which differ from the already existing ones.