Need a little help in the following:
Let $f(z)$ analytic function on $D = \{z\in\mathbb C: |z| < 1\}$. Define $\displaystyle d = \sup_{z,w \in D} |f(z) - f(w)|$.
Prove that $|f'(0)| \leq \frac{d}{2}$.
Need a little help in the following:
Let $f(z)$ analytic function on $D = \{z\in\mathbb C: |z| < 1\}$. Define $\displaystyle d = \sup_{z,w \in D} |f(z) - f(w)|$.
Prove that $|f'(0)| \leq \frac{d}{2}$.