J. Korean Math. Soc. 2004; 41(1): 175-192
Printed January 1, 2004
Copyright © The Korean Mathematical Society.
Lawrence A. Harris
University of Kentucky
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.
Keywords: Banach space, Frechet derivative, convex domain, holomorphic numerical range, Bloch radii, Cartan uniqueness theorem
MSC numbers: 46G20, 46T25, 47H10, 47J07
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