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Math Help - show that f has a fixed point

  1. #1
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    show that f has a fixed point

    I think I am supposed to use Rouche Theorem and Cauchy Argument Principle for this problem as well:



    Any ideas? Any help is appreciated! thanks
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  2. #2
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    Define g(z) = f(z) - z and use Rouche's theorem by showing that g(z) has a zero in the disk. That will mean there is a\in D(0,1) such that g(a)=0\implies f(a) = a and hence f has a fixed point.
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