Let \(f\) be analytic on the disk \(\Delta(z_0,r)\) and suppose there is \(m>0\) such that \[ |f(z)-f(z_0)|\le m\qquad(z\in\Delta(z_0,r)). \] Prove \[ |f'(z_0)|\le \frac mr. \]
A Cauchy derivative estimate at the center of a disk
P-WESCA09-III1
- Area
- Complex Analysis
- Seen at
- WESLEYAN
- Years
- 2009
- Status
- draft