Abstract and Applied Analysis
Volume 2003 (2003), Issue 5, Pages 261-274

Fixed points of holomorphic mappings for domains in Banach spaces

Lawrence A. Harris

Department of Mathematics, University of Kentucky, Lexington 40506, KY, USA

Received 29 November 2001

Copyright © 2003 Lawrence A. Harris. 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.


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.