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International Journal of Differential Equations
Volume 2013 (2013), Article ID 268309, 4 pages
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.
- J. van Neerven, The Asymptotic Behaviour of Semigroups of Linear Operators, vol. 88 of Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 1996.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- C. Corduneanu, Almost Periodic Oscillations and Waves, Springer, New York, NY, USA, 2009.
- A. S. Besicovitch, Almost Periodic Functions, Dover Publications, New York, NY, USA, 1955.
- R. G. Douglas, Banach Algebra Techniques in Operator Theory, vol. 179 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 2nd edition, 1998.
- 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.
- 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.