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An example in holomorphic fixed point theory


Author: Monika Budzynska
Journal: Proc. Amer. Math. Soc. 131 (2003), 2771-2777
MSC (2000): Primary 32A10, 46G20, 47H09, 47H10
Published electronically: March 11, 2003
MathSciNet review: 1974334
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Abstract: If $B$ is the open unit ball in the Cartesian product $l^2 \times l^2$ furnished with the $l^p$-norm $\Vert\cdot\Vert$, where $1 <p < \infty$ and $ p \neq 2$, then a holomorphic self-mapping $f$ of $B$ has a fixed point if and only if $\sup_{n\in \mathbb{N}} \Vert f^n (x)\Vert <1$ for some $x\in B.$


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Additional Information

Monika Budzynska
Affiliation: Instytut Matematyki UMCS, 20-031 Lublin, Poland
Email: monikab@golem.umcs.lublin.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06982-X
Keywords: Fixed points, holomorphic mappings, $k_D$-nonexpansive mappings, the Kobayashi distance, strict convexity, uniform convexity
Received by editor(s): March 28, 2001
Received by editor(s) in revised form: April 3, 2001, and March 29, 2002
Published electronically: March 11, 2003
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2003 American Mathematical Society