# Homework Help: Complex analysis - Schwarz's Lemma

1. Apr 13, 2012

### d2j2003

1. The problem statement, all variables and given/known data

Show that M|$\frac{f(z)-f(z_{0})}{M^2-\overline{f(z_{0})}f(z)}$|≤|$\frac{z-z_{0}}{1-\overline{z_{0}}z}$|

for all z, z$_{0}$ in {w:|w|<1|

2. Relevant equations

I think I will have to use Schwarz's Lemma: if f is analytic in disc |z|<1, f(0)=0, and |f(z)|≤1 for all z in the disc, then |f(z)|≤|z| , |z|<1

3. The attempt at a solution

This looks similar to Schwarz Pick Theorem (found online, don't completely understand..)

but one of the steps they used was to fix z which would mean that f(z)=z so the equations would become M|$\frac{z-f(z_{0})}{M^2-\overline{f(z_{0})}z}$|≤|$\frac{f(z)-z_{0}}{1-\overline{z_{0}}f(z)}$| or M|$\frac{z-f(z_{0})}{M^2-\overline{f(z_{0})}z}$|≤|$\frac{z-z_{0}}{1-\overline{z_{0}}z}$| not sure how that would help though...

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