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.

Show me the PDF file (215K), TEX file, and other files for this article.

Constantin Buse Department of Mathematics West University of Timisoara Bd. V. Parvan 4 1900 Timisoara, Romania e-mail: buse@hilbert.math.uvt.ro http://rgmia.vu.edu.au/BuseCVhtml/index.html | |

Sever S. Dragomir School of Communications and Informatics Victoria University of Technology PO Box 14428 Melburne City MC 8001 Victoria, Australia e-mail: sever@matilda.vu.edu.au http://rgmia.vu.edu.au/SSDragomirWeb.html |

Return to the EJDE web page