Abstract and Applied Analysis

Abstract and Applied Analysis / 2003 / Article

Open Access

Volume 2003 |Article ID 121329 | https://doi.org/10.1155/S1085337503205042

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

Received29 Nov 2001

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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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