Strong convergence theorems for multi-step Noor iterations with errors in Banach spaces

In this paper, we established two strong convergence theorems for a multi-step Noor iterative scheme with errors for mappings of asymptotically nonexpansive in the intermediate sense(asymptotically quasinonexpansive, respectively) in Banach spaces. Our results extend and improve the recent ones announced by Xu and Noor [B.L. Xu, M.A. Noor, Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces, J.Math. Anal. Appl. 267 (2002) 444–453], Cho, Zhou and Guo [Y.J. Cho, H. Zhou, G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47 (2004) 707–717], and many others. © 2005 Elsevier Inc. All rights reserved.