Asymptotically (omega,c)-periodic mild solutions to integro-differential equations

Abstract

In this paper, we are interested in the (recently introduced by Alavrez et al.) concept of the so-called asymptotically $(\omega,c)$ - periodic functions. We investigate further properties of this class of functions which complement the currently known ones. These properties allowed us to prove the existence and uniqueness of asymptotically ($\omega$,c) - periodic mild solution of an integro-differential equation in a Banach space, a result which generalizes some recent works in the class of S-asymptotically $\omega$- periodic functions by Brindle and N'Gu\'er\'ekata.