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Journal of Applied Mathematics
Volume 2014, Article ID 984946, 9 pages
http://dx.doi.org/10.1155/2014/984946
Research Article

Discrete Weighted Pseudo-Almost Automorphy and Applications

Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, Zhejiang 310023, China

Received 12 September 2013; Accepted 27 January 2014; Published 3 March 2014

Academic Editor: Francisco J. Marcellán

Copyright © 2014 Zhinan Xia. 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 deal with discrete weighted pseudo almost automorphy which extends some classical concepts and systematically explore its properties in Banach space including a composition result. As an application, we establish some sufficient criteria for the existence and uniqueness of the discrete weighted pseudo almost automorphic solutions to the Volterra difference equations of convolution type and also to nonautonomous semilinear difference equations. Some examples are presented to illustrate the main findings.