An example in holomorphic fixed point theory
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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 $\|\cdot \|$, where $1 <p < \infty$ and $p \neq 2$, then a holomorphic self-mapping $f$ of $B$ has a fixed point if and only if $\sup _{n\in \mathbb {N}} \|f^n (x)\| <1$ for some $x\in B.$References
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Additional Information
- Monika Budzyńska
- Affiliation: Instytut Matematyki UMCS, 20-031 Lublin, Poland
- Email: monikab@golem.umcs.lublin.pl
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2771-2777
- MSC (2000): Primary 32A10, 46G20, 47H09, 47H10
- DOI: https://doi.org/10.1090/S0002-9939-03-06982-X
- MathSciNet review: 1974334