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Math Help - Complex Analysis -analytic function

  1. #1
    Junior Member
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    Complex Analysis -analytic function

    Hello!
    Help me with this problem please.

    Thanks!


    Let f(z) be an analytic function in D=\left \{ z:\left | z \right | <1\right \}.
    Assume that d=\underset{z,w\in D}{sup} \left | f(z)-f(w) \right |.

    Prove that:  \left | f'(0) \right |\leqslant d/2
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Complex Analysis -analytic function

    Hint Use the Cauchy inequalities to g(z)=f(z)-f(0) for n=1.
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