hi, i have a function analytic on $D=\overline{B_1(0)}$ , $d = max_{z,w \in D} \{|f(z) - f(w)| \}$ , i need to prove that $2|f'(0)| \le d$.
So the hint is to define $F(z) = \dfrac{f(z)-f(-z)}{d}$.
I can see the $F :D \to D$ and we actually need to prove $|F'(0)| \le 1$. but im not sure how.. someone can help?