Fixed point iteration processes for asymptotic pointwise nonexpansive mappings in Banach spaces

Let X be a uniformly convex Banach space with the Opial property. Let T : C → C be an asymptotic pointwise nonexpansive mapping, where C is bounded, closed and convex subset of X. In this paper, we prove that the generalized Mann and Ishikawa processes converge weakly to a fixed point of T. In addition, we prove that for compact asymptotic pointwise nonexpansive mappings acting in uniformly convex Banach spaces, both processes converge strongly to a fixed point.