A Set of asymptotially almost automorphic functions

Abstract

For a set S of real numbers we introduce the concept of S-asymptotically almost automorphic functions valued in a Banach space.

It generalizes in particular the one of Z-asymptotically almost automorphic functions. This enables us to study the existence of

asymptotically almost automorphic solutions of a differential equation with piecewise constant argument of generalized type.