Convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense

In this paper, we prove a strong convergence of Ishikawa scheme to a uniformly L-Lipschitzian and asymptotically pseudocontractive mappings in the intermediate sense. No compactness assumption is imposed either on T or C, and computation of intersection of closed convex sets C-n and Q(n) for each n >= 1 is not required. We also obtain convergence results in this direction for asymptotically strict pseudocontractive mappings in the intermediate sense. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings. (C) 2011 Elsevier Ltd. All rights reserved.