Proving |f'(z)|<=1 for Simply Connected Domains

chocok · May 16, 2006

If S is a domain that is simply connected for S not equal to complex plane and z is in D. Assume g maps D into itself and f(z)=z.
prove |f'(z)|<=1

how should I do this? nowhere near the desired result.. help!

matt grime · May 16, 2006

You might want to define D rather than let us assume that you mean the unit disc. It does however look a lot like Schwarz's Lemma, does it not?

Proving |f'(z)|<=1 for Simply Connected Domains

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