Answer by Yiorgos S. Smyrlis for Analytic function $f$ in...
Cauchy's Integral Formula provides that$$f'\Big(\frac{1}{2}\Big)=\frac{1}{2\pi i}\int_{|z|=1}\!\frac{f(z)\,dz}{\big(z-\frac{1}{2}\!\big)^2},$$and hence\begin{align}\left\lvert\,...
View ArticleAnalytic function $f$ in $\overline{\mathbb{D}}$ satisfying...
Let $f$ be an analytic function on the closed unit disk $\overline{\mathbb{D}}$.On its boundary $\partial \mathbb{D}$ it holds that $\lvert\,f(z) -z\rvert < \lvert z\rvert$.I now have to show that...
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