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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:
54H25 Fixed-point and coincidence theorems (topological aspects)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
54C60 Set-valued maps in general topology
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