Convergence of an Ishikawa type iterative scheme for asymptotically quasi-nonexpansive mappings

In convex metric spaces, the Ishikawa iteration process and the Ishikawa iteration process with errors is defined for asymptotically quasi-nonexpansive mappings. It is proved some sufficient and necessary conditions for the iterative scheme converges to the fixed point of the asymptotically quasi-nonexpansive mappings. These results generalize and unify many important known results in recent literature.