Let K be a closed convex subset of an arbitrary real Banach space X，and T：K→K be a Lipschitz strictly pseudocontractive mapping such that T x*= x* for some x*∈X. Under the lack of the assumption that ＜∞，it is shown that the Ishikawa iterative sequence with errors engendered by xn+1=(1－αn) xn+αnTyn+un and yn＝(1－βn) xn+βnTxn+vn, for all n∈N，converges strongly to the unique fixed point of T. Moreover, this result provides a general converges rate estimate for such a sequence: if un=vn=0, for all n∈N，then we have ‖xn+1－x*‖≤(1－γn) ‖xn－x*‖≤…≤ (1－γj) ‖x0－x*‖，where ｛γj｝is a sequence in (0,1) such that for all n∈N, γn≥ min(ε，η－ε) αn. These results improve and generalize the recent corresponding results.