# Minimum of Closed, Continuous Analytic Function

Not what you're looking for? Search our solutions OR ask your own Custom question.

4. Let a function f be continuous in a closed bounded region R, and let it be analytic and not constant throughout the interior of R. Assuming that f(z) does not equal 0 anywhere in R, prove that f(z)f has a minimum value n in R which occurs on the boundary of R and never in the interior. Do this by applying the corresponding result for maximum values (Sec. 50) to the function g(z) = 1/f(z).

Please see the attached file for the fully formatted problem.

Â© BrainMass Inc. brainmass.com November 24, 2022, 11:59 am ad1c9bdddfhttps://brainmass.com/math/optimization/minimum-closed-continuous-analytic-function-34449

#### Solution Summary

The minimum of a closed, continuous analytic function is investigated.

$2.49