of asymptotically quasi-nonexpansive maps in convex metric spaces and CAT (0) spaces.
The new iteration scheme includes modified Mann and Ishikawa iterations, the three-step
iteration scheme of Xu and Noor and the scheme of Khan, Domlo and Fukhar-ud-din as
special cases in Banach spaces. Our results are refinements and generalizations of several
recent results from the current literature.