Summary: Let be a uniformly convex Banach space having a uniformly Gâteaux differentiable norm, a nonempty closed convex subset of , and a nonself multimap such that and is nonexpansive, where is the fixed point set of , is the family of nonempty compact subsets of and . Suppose that is a nonexpansive retract of and that, for each and , the contraction defined by has a fixed point . Let and be three real sequences in (0,1) satisfying approximate conditions. Then, for fixed and arbitrary , the sequence generated by
converges strongly to a fixed point of .