Liu Qihou, in 2001 and in 2002, extended the results of Petryshgh and Williamson, Ghosh and Debnath respectively in 1973 and in 1977, proved some sufficient and necessary condition for Ishikawa iterative sequence and for Ishikawa iterative sequence with error member of asymptotically quasi-nonenpansive mappings to converge to fixed poind in Banach space and in uniform convex Banach space. In convex metric spaces,the Ishikawa iteration process with errors is defined for asymptotically quasi-nonexpansive mappings.Some sufficient and nevessary conditions proved for the iterative schene converges to the fixed point of the asymptotically quasi-nonexpansire mappings.These results qeneralize and unify many important known results in recent literature.