Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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FIXED POINT THEOREMS FOR INFINITE DIMENSIONAL HOLOMORPHIC FUNCTIONS

  • Harris, Lwarence-A. (Department of Mathematics University of Kentucky Lexington)
  • Published : 2004.01.01
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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

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