Abstract
We establish three theorems which show that most of the bounded holomorphic self-mappings of a star-shaped domain in a complex Banach space map it strictly inside itself. According to the Earle–Hamilton fixed point theorem, each such mapping has a unique fixed point.
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Acknowledgments
The research of the first author was partially supported by the Technion VPR Fund. Both authors thank the referee for several pertinent comments.
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Communicated by David Shoikhet.
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Reich, S., Zaslavski, A.J. Three Generic Results in Holomorphic Fixed Point Theory. Complex Anal. Oper. Theory 8, 51–56 (2014). https://doi.org/10.1007/s11785-012-0266-2
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DOI: https://doi.org/10.1007/s11785-012-0266-2