Fixed points of holomorphic mappings for domains in Banach spaces

Lawrence A. Harris

Abstract and Applied Analysis, 2003, vol. 2003, 1-14

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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:121329

DOI: 10.1155/S1085337503205042

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