About this Journal Submit a Manuscript Table of Contents
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.

Linked References

  1. J. van Neerven, The Asymptotic Behaviour of Semigroups of Linear Operators, vol. 88 of Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  2. C. Chicone and Y. Latushkin, Evolution Semigroups in Dynamical Systems and Differential Equations, vol. 70 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1999. View at MathSciNet
  3. S. Clark, Y. Latushkin, S. Montgomery-Smith, and T. Randolph, “Stability radius and internal versus external stability in Banach spaces: an evolution semigroup approach,” SIAM Journal on Control and Optimization, vol. 38, no. 6, pp. 1757–1793, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. O. Saierli, “Spectral mapping theorem for an evolution semigroup on a space of vector-valued almost-periodic functions,” Electronic Journal of Differential Equations, vol. 2012, no. 175, pp. 1–9, 2012. View at MathSciNet
  5. C. Buşe, D. Lassoued, T. L. Nguyen, and O. Saierli, “Exponential stability and uniform boundedness of solutions for nonautonomous periodic abstract Cauchy problems. An evolution semigroup approach,” Integral Equations and Operator Theory, vol. 74, no. 3, pp. 345–362, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  6. C. Buşe, S. S. Dragomir, and V. Lupulescu, “Characterizations of stability for strongly continuous semigroups by boundedness of its convolutions with almost periodic functions,” International Journal of Differential Equations and Applications, vol. 2, no. 1, pp. 103–109, 2001. View at MathSciNet
  7. A. Zada, G. Rahmat, G. Ali, and A. Tabassum, “Characterizations of stability for discrete semigroup of bounded linear operators,” International Journal of Mathematics and Soft Computing, vol. 3, no. 3, 2013.
  8. C. Buşe and O. Jitianu, “A new theorem on exponential stability of periodic evolution families on Banach spaces,” Electronic Journal of Differential Equations, vol. 2013, no. 14, pp. 1–10, 2003. View at Zentralblatt MATH · View at MathSciNet
  9. C. Corduneanu, Almost Periodic Oscillations and Waves, Springer, New York, NY, USA, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  10. A. S. Besicovitch, Almost Periodic Functions, Dover Publications, New York, NY, USA, 1955. View at Zentralblatt MATH · View at MathSciNet
  11. R. G. Douglas, Banach Algebra Techniques in Operator Theory, vol. 179 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2nd edition, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  12. C. Buşe, A. Khan, G. Rahmat, and A. Tabassum, “Uniform exponential stability for nonautonomous system via discrete evolution semigroups,” to appear in Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie.
  13. C. Buşe, P. Cerone, S. S. Dragomir, and A. Sofo, “Uniform stability of periodic discrete systems in Banach spaces,” Journal of Difference Equations and Applications, vol. 11, no. 12, pp. 1081–1088, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet