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http://dx.doi.org/10.4134/JKMS.2004.41.1.175

FIXED POINT THEOREMS FOR INFINITE DIMENSIONAL HOLOMORPHIC FUNCTIONS  

Harris, Lwarence-A. (Department of Mathematics University of Kentucky Lexington)
Publication Information
Journal of the Korean Mathematical Society / v.41, no.1, 2004 , pp. 175-192 More about this Journal
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 unique-ness theorem.
Keywords
Banach space; Frechet derivative; convex domain; holo-morphic numerical range; Bloch radii; Cartan ununiqueness theorem;
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