Abstract: The common fixed points of two finite families of
set-valued asymptotically nonexpansive mappings were studied in real
uniformly convex Banach spaces. A finite-step iteration process for
these two families was introduced, and some strong convergence
theorems for this scheme were proved. The results improve and extend
some recent relative results.

Key words: uniformly convex Banach space, set-valued asymptotically nonexpansive mapping, finite-step iteration process, common fixed points