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An example in holomorphic fixed point theory
Authors:Monika Budzynska
Affiliation:Instytut Matematyki UMCS, 20-031 Lublin, Poland
Abstract:If $B$ is the open unit ball in the Cartesian product $l^2 times l^2$ furnished with the $l^p$-norm $VertcdotVert$, where $1 <p < infty$ and $ p neq 2$, then a holomorphic self-mapping $f$ of $B$ has a fixed point if and only if $sup_{nin mathbb{N}} Vert f^n (x)Vert <1$ for some $xin B.$

Keywords:Fixed points   holomorphic mappings   $k_D$-nonexpansive mappings   the Kobayashi distance   strict convexity   uniform convexity
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