#### You've reached the end of your free preview.

Want to read the whole page?

**Unformatted text preview: **π/ 2-1 e π/ 2 + 1 . 3. Let f : D (0 , 1) → C be analytic and | f ( z ) | < 1 for all z ∈ D (0 , 1). (a) Show that | f ( z ) | 1- | f ( z ) | 2 ≤ 1 1- | z | 2 . (b) Suppose there exist two distinct points a,b ∈ D (0 , 1) such that f ( a ) = a and f ( b ) = b . Show that f ( z ) = z for all z ∈ D (0 , 1). (c) Suppose there exist a ∈ D (0 , 1), a 6 = 0, such that f ( a ) = 0 = f (-a ). Show that | f (0) | ≤ | a | 2 . What can you conclude if | f (0) | = | a | 2 ? Date : November 8, 2007 (Version 1.2); posted: November 8, 2007; due: November 14, 2007. 1...

View
Full Document

- Fall '07
- Lim
- Math, Analytic function, Entire function, |F