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On asymptotic pointwise contractions in metric spaces. (English) Zbl 1176.54031
Let $M$ be a complete CAT(0) metric space and $C$ be a nonempty bounded closed convex subset of it. Then, for each pointwise asymptotically nonexpansive map $T:C\to C$, $\text{Fix}(T)$ is nonempty, closed and convex.

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
47H09Mappings defined by “shrinking” properties
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
54C60Set-valued maps (general topology)
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References:
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