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.
|Number of pages||14|
|Journal||Abstract and Applied Analysis|
|State||Published - Mar 10 2003|
ASJC Scopus subject areas
- Applied Mathematics