A unique solution of initial value problems for first order impulsive integro-differential equations of mixed type in Banach spaces

Abstract

In this paper, we investigate initial value problem for first order impulsive integro-differential equation of mixed type in a Banach space. Without any compactness-type assumption, we obtain a unique solution of the equation, an explicit iterative approximation of the solution and an error estimate of the approximation sequence. Our result improves and extends many recent results.