Pointwise Lipschitzian mappings in uniformly convex and uniformly smooth Banach spaces

Let XX be a uniformly convex and uniformly smooth Banach space. Let T:C→CT:C→C be an asymptotic pointwise nonexpansive mapping, where CC is a bounded, closed and convex subset of XX. In this paper we investigate conditions sufficient for the weak convergence of the generalized Mann and Ishikawa processes to a fixed point of TT.