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Abstract and Applied Analysis
Volume 2014, Article ID 784289, 4 pages
http://dx.doi.org/10.1155/2014/784289
Research Article

Uniform Exponential Stability of Discrete Evolution Families on Space of -Periodic Sequences

1School of Informatics, Linyi University, Linyi, Shandong 276005, China
2Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
3Laboratoire SAMM EA4543, Université Paris 1 Panthéon-Sorbonne, Centre P. M. F., 90 Rue de Tolbiac, 75634 Paris Cedex 13, France

Received 28 April 2014; Revised 30 June 2014; Accepted 1 July 2014; Published 31 August 2014

Academic Editor: Qi-Ru Wang

Copyright © 2014 Yongfang Wang et al. 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 prove that the discrete system is uniformly exponentially stable if and only if the unique solution of the Cauchy problem , , is bounded for any real number and any -periodic sequence with . Here, is a sequence of bounded linear operators on Banach space .