Pseudo asymptotically periodic solutions for Volterra integro-differential equations

In this paper, we propose a new class of functions called pseudo S-asymptotically -periodic function in the Stepanov sense and explore its properties in Banach spaces including composition results. Furthermore, the existence and uniqueness of the pseudo S-asymptotically -periodic mild solutions to Volterra integro-differential equations is investigated. Applications to integral equations arising in the study of heat conduction in materials with memory are shown. Copyright (c) 2014 John Wiley & Sons, Ltd.