Abstract
This talk discusses conditions on the numerical range of a holomorphic function defined on a bounded convex domain in a complex Banach space that imply that the function has a unique fixed point. In particular, extensions of the Earle-Hamilton Theorem are given for such domains. The theorems are applied to obtain a quantitative version of the inverse function theorem for holomorphic functions and a distortion form of Cartan's uniqueness theorem.
| Original language | English |
|---|---|
| Pages (from-to) | 175-192 |
| Number of pages | 18 |
| Journal | Journal of the Korean Mathematical Society |
| Volume | 41 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2004 |
Keywords
- Banach space
- Bloch radii
- Cartan uniqueness theorem
- Convex domain
- Fréchet derivative
- Holomorphic numerical range
ASJC Scopus subject areas
- General Mathematics
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