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.
Digital Object Identifier (DOI)
Harris, Lawrence A., "Fixed Points of Holomorphic Mappings for Domains in Banach Spaces" (2003). Mathematics Faculty Publications. 41.