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- W4300775964 abstract "Let $D$ be a bounded domain in a complex Banach space. According to the Earle-Hamilton fixed point theorem, if a holomorphic mapping $F : D mapsto D$ maps $D$ strictly into itself, then it has a unique fixed point and its iterates converge to this fixed point locally uniformly. Now let $mathcal{B}$ be the open unit ball in a complex Hilbert space and let $F : mathcal{B} mapsto mathcal{B}$ be holomorphic. We show that a similar conclusion holds even if the image $F(mathcal{B})$ is not strictly inside $mathcal{B}$, but is contained in a horosphere internally tangent to the boundary of $mathcal{B}$. This geometric condition is equivalent to the fact that $F$ is asymptotically strongly nonexpansive with respect to the hyperbolic metric in $mathcal{B}$." @default.
- W4300775964 created "2022-10-04" @default.
- W4300775964 creator A5054324944 @default.
- W4300775964 date "2011-05-14" @default.
- W4300775964 modified "2023-09-26" @default.
- W4300775964 title "A generalized version of the Earle-Hamilton fixed point theorem for the Hilbert ball" @default.
- W4300775964 doi "https://doi.org/10.48550/arxiv.1105.2877" @default.
- W4300775964 hasPublicationYear "2011" @default.
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