Abstract
We discuss the Earle-Hamilton fixed-point theorem and show how it can be applied when restrictions are known on the numerical range of a holomorphic function. In particular, we extend the Earle-Hamilton theorem to holomorphic functions with numerical range having real part strictly less than 1. We also extend the Lumer-Phillips theorem estimating resolvents to dissipative holomorphic functions.
Document Type
Article
Publication Date
2003
Digital Object Identifier (DOI)
https://doi.org/10.1155/S1085337503205042
Repository Citation
Harris, Lawrence A., "Fixed Points of Holomorphic Mappings for Domains in Banach Spaces" (2003). Mathematics Faculty Publications. 41.
https://uknowledge.uky.edu/math_facpub/41
Notes/Citation Information
Published in Abstract and Applied Analysis, v. 2003, issue 5, p. 261-274.
Copyright © 2003 Hindawi Publishing Corporation
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.