Fixed point iteration processes for asymptotically nonexpansive mappings

Let X be a uniformly convex Banach space which satisfies Opial’s condition or has a Frèchet differentiable norm, C a bounded closed convex subset of X, and T: C → C an asymptotically nonexpansive mapping. It is then shown that the modified Mann and Ishikawa iteration processes defined by respectively, converge weakly to a fixed point of T. © 1994 American Mathematical Society.