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    Minimum Value of Closed, Continuous Analytic Function

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    5. Use the function f(z) = z to show that in Exercise 4 the condition f(z) does not equal 0 anywhere in P is necessary in order to obtain the result of that exercise. That is, show that |f(z)| can reach its minimum value at an interior point when that minimum value is zero.

    Please see the attached file for Exercise 4 and the fully formatted problem.

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    Proof. Consider the function f(z)=z and a closed bounded region , namely, a unit disk. Obviously, is continuous and ...

    Solution Summary

    The Minimum Value of a Closed, Continuous Analytic Function is investigated.