On S-asymptotically ω-periodic functions on Banach spaces and applications

This paper is devoted to the study of the class of continuous and bounded functions f : [0,∞)→X for which exists ω>0 such that limt→∞(f (t +ω)−f (t)) = 0 (in the sequel called S-asymptotically ω-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically ω-periodic functions.We also study the existence of S-asymptotically ω-periodic mild solutions of the first-order abstract Cauchy problem in Banach spaces. © 2008 Elsevier Inc. All rights reserved