International Journal of Mathematics and Mathematical Sciences 
Volume 2004 (2004), Issue 61, Pages 3237-3247
doi:10.1155/S016117120440653X

On some classes of almost periodic functions in abstract spaces

Dariusz Bugajewski1 and Gaston M. N'Guérékata2

 1Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, Poznań 61-614, Poland
2Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA
Received 15 August 2004

Abstract

We deal with C(n)-almost periodic functions taking values in a Banach space. We give several properties of such functions, in particular, we investigate their behavior in view of differentiation as well as integration. The superposition operator acting in the space of such functions is also under consideration. Some applications to ordinary as well as partial differential equations are presented. Moreover, we introduce the class of the so-called asymptotically C(n)-almost periodic functions and give some of their properties.