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Zbl 1176.54031
Hussain, N.; Khamsi, M.A.
On asymptotic pointwise contractions in metric spaces.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 71, No. 10, A, 4423-4429 (2009). ISSN 0362-546X

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.
[Mihai Turinici (Iaşi)]
MSC 2000:
*54H25 Fixed-point theorems in topological spaces
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
54C60 Set-valued maps

Keywords: asymptotic pointwise contraction; nonexpansive (multivalued) map; fixed point; hyperconvex and uniformly convex metric space; CAT(0) spaces

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