Td. Benavides et Pl. Ramirez, Structure of the fixed point set and common fixed points of asymptoticallynonexpansive mappings, P AM MATH S, 129(12), 2001, pp. 3549-3557
Let X be a Banach space, C a weakly compact convex subset of X and T : C --
> C an asymptotically nonexpansive mapping. Under the usual assumptions on
X which assure the existence of fixed point for T, we prove that the set of
fixed points is a nonexpansive retract of C. We use this result to prove t
hat all known theorems about existence of fixed point for asymptotically no
nexpansive mappings can be extended to obtain a common fixed point for a co
mmuting family of mappings. We also derive some results about convergence o
f iterates.