Problem 1786 (difficulty: 7/10)

Assume that \(\displaystyle f\in O(|z|<1)\) has image \(\displaystyle \re z>0\), and \(\displaystyle f(0)=1\). Show that

\(\displaystyle \frac{1-|z|}{1+|z|}\le |f(z)|\le \frac{1+|z|}{1-|z|}.\)

Solution-->

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