Impulsive integro-differential equations with nonlocal conditions in Banach spaces

In this work, we give sufficient conditions for the existence of a mild solution for some impulsive integro-differential equations in Banach spaces. We study the existence without assuming the Lipschitz condition on the nonlinear term $f$. The compactness on the $C_0\text{-}semigroup{\left(T\left(t\right)\right)}_{t\ge 0}$ in a Banach space is not needed. We use Hausdorff’s measure of noncompactness, resolvent operators and Darbo’s fixed point Theorem to obtain the main result of this work.