Weak and Strong Convergence of Finite Family with Errors of Nonexpansive Nonself-mappings

Let K be a subset of a real normed linear space E and let T be a self-mapping on K . T is said to be nonexpansive provided ‖Tx−Ty‖ ‖x− y‖ for all x, y ∈ K . Fixed-point iteration process for nonexpansive mappings in Banach spaces including Mann and Ishikawa iteration processes has been studied extensively by many authors to solve the nonlinear operator equations in Hilbert spaces and Banach spaces; see [3, 7, 10, 11, 15, 16]. Tan and Xu [15] introduced and studied a modified Ishikawa process to approximate fixed points of nonexpansive mappings defined on nonempty closed convex bounded subsets of a uniformly convex Banach space E. Five years later, Xu [18] introduced iterative schemes known as Mann iterative scheme with errors and Ishikawa iterative scheme with errors. Takahashi and Tamura [14] introduced and studied a generalization of Ishikawa iterative schemes for a pair of nonexpansive mappings in Banach spaces. Recently, Khan and Fukhar-ud-din [6] extended their scheme to the modified Ishikawa iterative schemes with errors for two mappings and gave weak and strong convergence theorems. On the other hand, iterative techniques for approximating fixed points of nonexpansive nonself-mappings have been studied by various authors; see [4, 8, 13, 19]. Shahzad [12] introduced and studied an iteration scheme for