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# 7 . Suppose f is continuous on D and holomorphic on D- (a Show that |fl attains its maximum 0n the boundary â‚¬D. That iS, show that there is w â‚¬ â‚¬D...

## Question

###### 7 . Suppose f is continuous on D and holomorphic on D- (a Show that |fl attains its maximum 0n the boundary â‚¬D. That iS, show that there is w â‚¬ â‚¬D such that |f(2)l < |f (w)l for every 2 â‚¬ D. (Hint: The assertion is clear if f is constant_ Assume f is not constant Since |f | is continuous on D which is a closed and bounded set) , by the extreme value theorem, |fl has a maximum 0n D. Can this maximum be in D? See the maximum modulus principle (Theorem 4.5, page 92 of Stein-Shakarchi).)

7 . Suppose f is continuous on D and holomorphic on D- (a Show that |fl attains its maximum 0n the boundary â‚¬D. That iS, show that there is w â‚¬ â‚¬D such that |f(2)l < |f (w)l for every 2 â‚¬ D. (Hint: The assertion is clear if f is constant_ Assume f is not constant Since |f | is continuous on D which is a closed and bounded set) , by the extreme value theorem, |fl has a maximum 0n D. Can this maximum be in D? See the maximum modulus principle (Theorem 4.5, page 92 of Stein-Shakarchi).)  #### Similar Solved Questions

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