Approximate controllability of stochastic impulsive functional systems with infinite delay

This paper studies the approximate controllability of stochastic impulsive functional system with infinite delay in abstract space. By using the contraction mapping principle, some sufficient conditions are given with no compactness condition imposed on the semigroup generated by the linear part of the system. Then with the help of the Nussbaum fixed point theorem, the restriction of the combination of system parameters is dropped. Finally, an example is shown to illustrate our results.