LAUSR

In this paper, we explore the asymptotic average shadowing property of iterated function systems. We show that for an iterated function system IFS $$(\mathscr {F})$$ such that one of $$\mathscr {F}$$ is surjective, the pseudo-orbital specification implies the asymptotic average shadowing, and by this result, we obtain that the ergodic shadowing implies the asymptotic average shadowing. Moreover, we also prove that the asymptotic average shadowing implies the average shadowing. Furthermore, we give criteria for an iterated function system that does not have the asymptotic average shadowing property.