Buse, ConstantinDragomir, Sever S.2020-02-192020-02-192001-06-20Buse, C., & Dragomir, S. S. (2001). A new proof for a Rolewicz's type theorem: An evolution semigroup approach. <i>Electronic Journal of Differential Equations, 2001</i>(45), pp. 1-5.1072-6691https://hdl.handle.net/10877/9314Let φ be a positive and non-decreasing function defined on the real half-line and U be a strongly continuous and exponentially bounded evolution family of bounded linear operators acting on a Banach space. We prove that if φ and U satisfy a certain integral condition (see the relation (2) below) then U is uniformly exponentially stable. For φ continuous, this result is due to S. Rolewicz.Text5 pages1 file (.pdf)enAttribution 4.0 InternationalEvolution family of bounded linear operatorsEvolution operator semigroupRolewicz's theoremArticle