Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces

Let ( M , d ) be a complete 2-uniformly convex metric space. Let C be a nonempty, bounded, closed, and convex subset of M , and let T : C → C be an asymptotic pointwise nonexpansive mapping. In this paper, we prove that the modified Mann iteration process defined by x n + 1 = t n T n ( x n ) ⊕ ( 1 − t n ) x n converges in a weaker sense to a fixed point of T .