Mann iteration process for asymptotic pointwise nonexpansive mappings in metric spaces

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