Abstract: In this paper, by a new technique, the author study the problem for the Ishikawa iterative sequence in the general Banach space, and obtains some new results, removes the strict condign of the space being uniformly smooth as usual, in addition, removes or weakens the other some condition, and so improves a series of corresponding theorems in recent pa-pers ^[1-7].

Key words: Ishikawa iteration, (local) Strongly accretive operator, (local) Strongly pseudocontractive operator