Linear integral equations with asymptotically almost periodic solutions

Conditions are given that ensure that bounded solutions of $\text{∫}{}_{\mathrm{?\xi }}{}^{\mathrm{\xi }}\text{x(t ? ξ)dA(ξ) = ?(t)}$ are asymptotically almost periodic. The result strengthens and extends a recent theorem of Levin and Shea. Generalizations to systems of integral equations as well as to integrodifferential systems are included.