  In this paper, we show the existence of function which is not
S-asymptotically omega-periodic, but which is S-asymptotically omega-periodic
in the Stepanov sense. We give sufficient conditions for the existence and
uniqueness of S-asymptotically omega-periodic solutions for a nonautonomous
differential equation with piecewise constant argument in a Banach space when
omega is an integer. This is done using the Banach fixed point Theorem. An
example involving the heat operator is discussed as an illustration of the
theory.
