Hyers–Ulam stability of impulsive integral equations

In this manuscript, first we study the Hyers–Ulam stability of linear impulsive Volterra integral equations with the help of open mapping theorem approach. Then we give an existence and uniqueness theorem for the solutions of a class of nonlinear impulsive integral equations with a bounded variable delay. Moreover, with the help of integral inequality of Gronwall type, we investigate the Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the same class of integral equations. We also present examples to support our main results.