Viscosity iterative method for a finite family of generalized asymptotically quasi-nonexpansive mappings in convex metric spaces

We introduce a general viscosity iterative method for a finite family of generalized asymptotically quasi-nonexpansive mappings in a convex metric space. The new iterative method contains several well-known iterative methods as its special case including multistep iterative method of Khan et al. [Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach space, J. Math. Anal. Appl. 341(2008), 1-11] and viscosity iterative method of Chang et al. [Approximating solutions of variational inequalities for asymptotically nonexpansive mappings, Appl. Math. Comput., 212(2009), 51-59]. Our results are new in convex metric spaces and generalize many known results in Banach spaces and CAT(0) spaces simultaneously.