A new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex metric spaces

Sufficient conditions for the convergence of a new multistep iteration to a common fixed point of a finite family of asymptotically quasinonexpansive mappings in the framework of convex metric spaces are obtained. As an application, related results for a new three step iteration are derived. Our convergence results generalize and refine many known results.