A study on asymptotically almost automorphic solution of impulsive Volterra integro-differential equation

Abstract

This article deals with the concept of existence of piecewise continuous asymptotically almost automorphic $\mathcal{(AAA)}$ solution of impulsive volterra integro-differential equation. To study this, we first introduce several notions about $\mathcal{AAA}$ type functions and obtain some properties of such functions. The working rules are based on suitable Lipschitz conditions and the results are proved by Krasnoselskii's fixed point theorem of bounded linear operators. An example is shown to exhibit our analytic findings.