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FIXED POINT THEOREMS FOR INFINITE DIMENSIONAL HOLOMORPHIC FUNCTIONS
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 Title & Authors
FIXED POINT THEOREMS FOR INFINITE DIMENSIONAL HOLOMORPHIC FUNCTIONS
Harris, Lwarence-A.;
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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 unique-ness theorem.
 Keywords
Banach space;Frechet derivative;convex domain;holo-morphic numerical range;Bloch radii;Cartan ununiqueness theorem;
 Language
English
 Cited by
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Abel averages and holomorphically pseudo-contractive maps in Banach spaces, Journal of Mathematical Analysis and Applications, 2015, 423, 2, 1580  crossref(new windwow)
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