0
$\begingroup$

Let $f:D \to D$ be holomorphic where $D$ is the unit disk and such that $f(1/2)=1/2$. Show $|f'(1/2)| \le 3/4$.

I've used various forms of the Schwarz lemma and Schwarz-pick lemma via composing with the automorphism sending 1/2 to 0, but I'm still only able to prove that $|f'(1/2)| \le 1$ (which it itself is a corollary to Schwarz lemma in my text). Any suggestions?

$\endgroup$
3
$\begingroup$

The function $f(z) = z$ would appear to be a counterexample.

$\endgroup$
2
  • $\begingroup$ I'm going to stick my neck out and say that in fact it is a counterexample... $\endgroup$ – David C. Ullrich Aug 27 '16 at 0:43
  • $\begingroup$ lol David $\,\,$ $\endgroup$ – zhw. Aug 27 '16 at 1:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.