C. Buse & S. S. Dragomir
Let be a positive and non-decreasing function defined on the real half-line and be a strongly continuous and exponentially bounded evolution family of bounded linear operators acting on a Banach space. We prove that if and satisfy a certain integral condition (see the relation (2) below) then is uniformly exponentially stable. For continuous, this result is due to S. Rolewicz.
Submitted May 14, 2001. Published June 20, 2001.
Math Subject Classifications: 47A30, 93D05, 35B35, 35B40, 46A30.
Key Words: Evolution family of bounded linear operators, evolution operator semigroup, Rolewicz's theorem.
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|Constantin Buse |
Department of Mathematics
West University of Timisoara
Bd. V. Parvan 4
1900 Timisoara, Romania
|Sever S. Dragomir |
School of Communications and Informatics
Victoria University of Technology
PO Box 14428
Melburne City MC 8001
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