Let be a function which is analytic on and inside the circle and which satisfies for all on the circle . Prove that .

By Cauchy's inequality i managed to obtain

.

How do i proceed to prove that ? Any help/suggestion is welcome!:D

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- Nov 16th 2012, 03:22 AMalphabeta89help for question on bound of f(0)
Let be a function which is analytic on and inside the circle and which satisfies for all on the circle . Prove that .

By Cauchy's inequality i managed to obtain

.

How do i proceed to prove that ? Any help/suggestion is welcome!:D - Nov 16th 2012, 04:07 AMFernandoRevillaRe: help for question on bound of f(0)
- Nov 16th 2012, 04:13 AMhediRe: help for question on bound of f(0)
use the Cauchy integral formula to evaluate and estimate f(0) as an integral over the unit circle.

- Nov 16th 2012, 04:17 AMalphabeta89Re: help for question on bound of f(0)
- Nov 16th 2012, 05:04 AMhediRe: help for question on bound of f(0)
Yes,see attached.

- Nov 16th 2012, 05:15 AMalphabeta89Re: help for question on bound of f(0)