Fixed point theorems for infinite dimensional holomorphic functions

Lawrence A. Harris

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish
Pages (from-to)175-192
Number of pages18
JournalJournal of the Korean Mathematical Society
Issue number1
StatePublished - 2004


  • Banach space
  • Bloch radii
  • Cartan uniqueness theorem
  • Convex domain
  • Fréchet derivative
  • Holomorphic numerical range

ASJC Scopus subject areas

  • Mathematics (all)


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