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Fixed Point Theorems For Infinite Dimensional Holomorphic Functions, Lawrence A. Harris
Fixed Point Theorems For Infinite Dimensional Holomorphic Functions, Lawrence A. Harris
Mathematics Faculty Publications
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.