Lawrence A. Harris, "Fixed points of holomorphic mappings for domains in Banach spaces", Abstract and Applied Analysis, vol. 2003, Article ID 121329, 14 pages, 2003. https://doi.org/10.1155/S1085337503205042
Fixed points of holomorphic mappings for domains in Banach spaces
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.
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