Let X be a real Banach space and $A:X{ ightarrow}2^X$ be an $alpha$-strongly accretive operator. It is proved that if the duality mapping J of X satisfies Condition (I) with additional conditions, then the Ishikawa and Mann iteration processes with errors converge strongly to the unique solution of operator equation $z{in}Ax$. In addition, the convergence of the Ishikawa and Mann iteration processes with errors for $alpha$-strongly pseudo-contractive operators is given.