Open Access
10 March 2003 Fixed points of holomorphic mappings for domains in Banach spaces
Lawrence A. Harris
Abstr. Appl. Anal. 2003(5): 261-274 (10 March 2003). DOI: 10.1155/S1085337503205042


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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Lawrence A. Harris. "Fixed points of holomorphic mappings for domains in Banach spaces." Abstr. Appl. Anal. 2003 (5) 261 - 274, 10 March 2003.


Published: 10 March 2003
First available in Project Euclid: 15 April 2003

zbMATH: 1034.47021
MathSciNet: MR1981265
Digital Object Identifier: 10.1155/S1085337503205042

Primary: 46T25 , 47H10
Secondary: 47A12

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 5 • 10 March 2003
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