Fixed point theorems for infinite dimensional holomorphic functions

Lawrence A. Harris

doi:10.4134/JKMS.2004.41.1.175

Fixed point theorems for infinite dimensional holomorphic functions

Lawrence A. Harris

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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 uniqueness theorem.

Original language	English
Pages (from-to)	175-192
Number of pages	18
Journal	Journal of the Korean Mathematical Society
Volume	41
Issue number	1
DOIs	https://doi.org/10.4134/JKMS.2004.41.1.175
State	Published - 2004

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.4134/JKMS.2004.41.1.175

Cite this

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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 uniqueness theorem.",

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AB - 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.

KW - Banach space

KW - Bloch radii

KW - Cartan uniqueness theorem

KW - Convex domain

KW - Fréchet derivative

KW - Holomorphic numerical range

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DO - 10.4134/JKMS.2004.41.1.175

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EP - 192

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 1

ER -

Fixed point theorems for infinite dimensional holomorphic functions

Abstract

Keywords

ASJC Scopus subject areas

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