Hi, I am in honors track Complex Analysis, and I think I've reached my limit. We got this proof, and I don't know where to start. "We saw in class that a mobius transformation can have at most one fixed point (or else is the identity map), extend this idea to all analytic functions mapping from a domain[itex]\subset[/itex]ℂ to itself." I have no idea what to do. I totally understand the mobius version of this, but it is way easier. I saw a similar problem online for the unit disk, but then you have Schwart's Lemma. I also had a couple other thoughts that led nowhere. |f(z)-z| attains a minimum at any fixed point. Rouche's theorem would be nice if we could say something about curves, but I don't know how to extend that to an arbitrary domain. Any push in the right direction would be appreciated.