Advances in Difference Equations
Volume 2011 (2011), Article ID 654695, 12 pages
doi:10.1155/2011/654695
Research Article

Composition Theorems of Stepanov Almost Periodic Functions and Stepanov-Like Pseudo-Almost Periodic Functions

Wei Long and Hui-Sheng Ding

College of Mathematics and Information Science, Jiangxi Normal University Nanchang, Jiangxi 330022, China

Received 31 December 2010; Accepted 20 February 2011

Academic Editor: Toka Diagana

Copyright © 2011 Wei Long and Hui-Sheng Ding. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish a composition theorem of Stepanov almost periodic functions, and, with its help, a composition theorem of Stepanov-like pseudo almost periodic functions is obtained. In addition, we apply our composition theorem to study the existence and uniqueness of pseudo-almost periodic solutions to a class of abstract semilinear evolution equation in a Banach space. Our results complement a recent work due to Diagana (2008).