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International Journal of Differential Equations
Volume 2013 (2013), Article ID 268309, 4 pages
http://dx.doi.org/10.1155/2013/268309
Research Article

On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups

1Shaheed Benazir Bhutto University Sheringal, Dir Upper 18000, Pakistan
2Government College University, Abdus Salam School of Mathematical Sciences (ASSMS), Lahore 54600, Pakistan
3Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan

Received 22 April 2013; Revised 19 June 2013; Accepted 20 June 2013

Academic Editor: Sotiris Ntouyas

Copyright © 2013 Aftab Khan 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 a discrete semigroup of bounded linear operators acting on a complex Banach space is uniformly exponentially stable if and only if, for each , the sequence belongs to . Similar results for periodic discrete evolution families are also stated.