Summary: Several weak and strong convergence theorems are established for a modified Noor iterative scheme with errors for three asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type, and Noor-type iterations are covered by the new iteration scheme. Our results extend and improve the recently announced ones [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.