Abstract and Applied Analysis
Volume 2003 (2003), Issue 5, Pages 261-274
doi:10.1155/S1085337503205042

Fixed points of holomorphic mappings for domains in Banach spaces

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.