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In this manuscript we investigate the existence of mild solution for a abstract impulsive neutral integro-differential equation by using semi-group theory and Krasnoselskii-Schaefer fixed point theorem in different approach. At last, an example is also provided to illustrate the obtained results.

In this paper we discussed about the approximate controllability of impulsive neutral integro-differential equations with deviated arguments and infinite delay. In the nonlinear term, we introduce the control parameter. The invertibility of the operator in infinite dimensional spaces is not possible if the generated semigroup is compact. So we remove to assume that concept and there is no need of Lipschitz continuity of nonlinear function. Finally suitable example is also given.

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