A general demiclosed principle is established for asymptotically nonexpansive mappings in CAT(0) spaces. As a consequence, the following Krasnoselskii-Mann fixed point result is established.
Theorem. Let be a bounded closed convex part of a complete CAT(0) space and be asymptotically nonexpansive, with the sequence satisfying . Then, for each and (with ), the iterative process
-converges to a fixed point of .