Uniform Convergence of the Sequence of Compositions

Hey everyone,

I need help with the following complex analysis problem. (It is from chapter 3 of Greene & Krantz):

Let $\displaystyle \phi : D(0,1) \mapsto D(0,1)$ be given by $\displaystyle \phi(z) = z + a_2 z^2 + a_3 z^3 + ...$ (notice in particular that $\displaystyle \phi$ is holomorphic). Let $\displaystyle \phi_1(z) = \phi(z), \phi_2(z) = \phi(\phi(z))$ and so on. Suppose that the sequence $\displaystyle \{ \phi_j \}$ converges uniformly on compact sets. Show that $\displaystyle \phi(z) = z$.

Any help is appreciated! Thank you