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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.
Document Type
Article
Publication Date
2004
Repository Citation
Harris, Lawrence A., "Fixed Point Theorems for Infinite Dimensional Holomorphic Functions" (2004). Mathematics Faculty Publications. 40.
https://uknowledge.uky.edu/math_facpub/40
Notes/Citation Information
Published in Journal of the Korean Mathematical Society, v. 41, no. 1, p. 175-192.
This article, Harris, L. A. (2004). Fixed point theorems for infinite dimensional holomorphic functions. Journal of the Korean Mathematical Society, 41(1), 175-192., was published by the Korean Mathematical Society and is available online at http://jkms.kms.or.kr. © Korean Mathematical Society.
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