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1)approximate total differentiability,½üËÆÈ«¿É΢ÐÔ

2)approximate differentiability,½üËÆ¿É΢ÐÔ

3)Approximability,¿É½üËÆÐÔ

4)approximate total differential,½üËÆȫ΢·Ö

5)approximate reachability,½üËÆ¿É´ïÐÔ

6)Approximate controllability,½üËÆ¿É¿ØÐÔ

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In this paper the density of solutions of the operator equation ª§y=y 0+LF(y)+LH(v)ª§ (L,H are linear operators and ª§Fª§ is nonlinear) is discussed by Banach fixed point theorem and Schauder fixed point theorem, then by the gotten results the approximate controllability of the semilinear systemª§ª§x¡ä(t)+A(t)x(t)=f(t,x(t))+Bu(t)ª§ª§on Banach space is studied.

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