Problem 1788 (difficulty: 7/10)

Let \(\displaystyle w:S(0, 1) \to S(0, 1)\) be regular and \(\displaystyle w(\alpha)=0\). Show that

(a) \(\displaystyle \displaystyle |w(z)|\le \left|\frac{z-\alpha}{1-\bar{\alpha}z}\right|\);       (b) \(\displaystyle |w'(a)|\le1-|\alpha|^2.\)

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