Uniform Exponential Stability of Discrete Semigroup and Space of Asymptotically Almost Periodic Sequences
Nisar Ahmad
University of Peshawar, PakistanHabiba Khalid
University of Peshawar, PakistanAkbar Zada
University of Peshawar, Pakistan
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Abstract
We prove that the discrete semigroup is uniformly exponentially stable if and only if for each the solution of the Cauchy problem
belongs to . Where is the algebraic generator of , is the set of all non-negative integers and is a complex Banach space. Our proof uses the approach of discrete evolution semigroups.
Cite this article
Nisar Ahmad, Habiba Khalid, Akbar Zada, Uniform Exponential Stability of Discrete Semigroup and Space of Asymptotically Almost Periodic Sequences. Z. Anal. Anwend. 34 (2015), no. 4, pp. 477–484
DOI 10.4171/ZAA/1550