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

Printable View

- November 16th 2012, 04:22 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 - November 16th 2012, 05:07 AMFernandoRevillaRe: help for question on bound of f(0)
- November 16th 2012, 05:13 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.

- November 16th 2012, 05:17 AMalphabeta89Re: help for question on bound of f(0)
- November 16th 2012, 06:04 AMhediRe: help for question on bound of f(0)
Yes,see attached.

- November 16th 2012, 06:15 AMalphabeta89Re: help for question on bound of f(0)