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    Complex analysis for Unit Circle

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    Let f be analytic inside and on the unit circle. Suppose that 0<|f(z)|<1 if |z| = 1.
    Show that f has exactly one fixed point inside the unit circle. ( note : a fixed point is a point Zo such that f(Zo) = Zo).

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    For |z| = 1 we have

    |-z| = 1 > |f(z)|

    So by Rouche's ...

    Solution Summary

    The expert examines a complex analysis for Unit Circles.