On the convergence of iteration processes for semigroups of nonlinear mappings in banach spaces

Let C be a bounded, closed, convex subset of a uniformly convex Banach space X. We investigate the convergence of the generalized Krasnosel’skii-Mann and Ishikawa iteration processes to common fixed points of pointwise Lipschitzian semigroups of nonlinear mappings T t : C → C. Each of T t is assumed to be pointwise Lipschitzian, that is, there exists a family of functions α t : C → [0,∞) such that ∥Tt(x)−Tt(y)∥≤αt(x)∥x−y∥ for x,y ∈ C