Summary: We introduce and study strong convergence of a general iteration scheme for a finite family of asymptotically quasi-nonexpansive maps in convex metric spaces and
spaces. The new iteration scheme includes modified Mann and Ishikawa iterations, the three-step iteration scheme of B.-L. Xu
and M. A. Noor
[J. Math. Anal. Appl. 267, No. 2, 444–453 (2002; Zbl 1011.47039
)] and the scheme of A. R. Khan, A. A. Domlo
and H. Fukhar-Ud-Din
[J. Math. Anal. Appl. 341, No. 1, 1–11 (2008; Zbl 1137.47053
)] as special cases in Banach spaces. Our results are refinements and generalizations of several recent results from the current literature.