Let be a nonempty closed convex subset of a real uniformly convex Banach space , which is also a nonexpansive retract of is a nonexpansive retraction of onto . Let be the sequence defined by , , , where is a nonexpansive mapping and , are sequences in for some . In the present paper, the author proves the following:
(1) If and the dual of has the Kadec-Klee property, then convergence weakly to some fixed point of .
(2) If and if there is a nondecreasing function with and for all such that for all , , then converges strongly to some fixed point of .