Let $X$ be a Banach space. Let $K$ be a nonempty subset of $X$. Let $T:K\to K$ be an $I$-asymptotically quasi-nonexpansive type mapping and $I:K\to K$ be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an $I$-asymptotically quasi-nonexpansive type mappping in Banach spaces to a common fixed point of $T$ and $I$. Also, we study the convergence of the Ishikawa iterative sequences to common fixed point for nonself $I$-asymptotically quasi-nonexpansive type mapping in Banach spaces. The results presented in this paper extend and generalize some recent work of Chang and Zhou [1], Wang [19], Yao and Wang [20] and many others.