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Journal of Function Spaces
Volume 2015, Article ID 953540, 10 pages
Research Article

Space of -Periodic Limit Functions and Its Applications to an Abstract Cauchy Problem

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 14 December 2014; Accepted 26 February 2015

Academic Editor: Ismat Beg

Copyright © 2015 Rui Xie and Chuanyi Zhang. 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 introduce a new space consisting of what we call -periodic limit functions. We investigate some properties of the new function space. In particular, we study inclusion relations among asymptotically periodic type function spaces. Finally, we apply the -periodic limit functions to investigate the existence and uniqueness of asymptotically -periodic mild solutions of an abstract Cauchy problem.