© Hindawi Publishing Corp. ISHIKAWA ITERATION PROCESS WITH ERRORS FOR NONEXPANSIVE MAPPINGS

Abstract. We study the construction and the convergence of the Ishikawa iterative pro-cess with errors for nonexpansive mappings in uniformly convex Banach spaces. Some recent corresponding results are generalized. 2000 Mathematics Subject Classification. 47H10, 40A05. 1. Introduction. Let C be a closed convex subset of a Banach space X and T: C → C be a nonexpansivemapping (i.e., ‖Tx−Ty ‖ ≤ ‖x−y ‖ for all x,y in C). Recently, Deng and Li [1] introduced an Ishikawa iteration sequence with errors as follows: for any given x0 ∈ C xn+1 =αnxn+βnTyn+γnun