Summary: We establish two strong convergence theorems for a multi-step Noor iterative scheme with errors for mappings which are asymptotically nonexpansive in the intermediate sense (or asymptotically quasi-nonexpansive, respectively) in Banach spaces. Our results extend and improve recent ones announced by B.–L. Xu
and M. A. Noor
[J. Math. Anal. Appl. 267, No. 2, 444–453 (2002; Zbl 1011.47039
)], Y. J. Cho, H.–Y. Zhou
and G.–T. Guo
, Comput. Math. Appl. 47, No. 4–5, 707–717 (2004; Zbl 1081.47063
)], and many others.