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