In this paper, we introduce two explicit one-step iterative procedures and use them to obtain weak and strong convergence theorems to a common fixed point of a finite family of non-self asymptotically quasi-nonexpansive mappings in real uniformly convex Banach spaces. Also, we establish weak and strong convergence theorems to a common fixed point of a finite family of non-self asymptotically nonexpansive mappings with respect to a sunny nonexpansive retraction P in real smooth uniformly convex Banach spaces. Our results extend and improve some known results