(6) Let f : U → C be analytic where U is an open domain that contains the closed unit disk; i.e., B1(0) CU. Suppose that |f(e")| < 1 for 0 < 0 < 27. Show that f has exactly one fixed point in the unit disk B1 (0); that is, the equation f(z) = z, || 2|| < 1 has precisely one solution.

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