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Applicable Analysis
An International Journal
Volume 84, 2005 - Issue 11
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Original Articles

Generalizations of a theorem of Rolewicz

Pages 1165-1172 | Published online: 04 Sep 2006
 

Abstract

The aim of this article is to give a unified treatment for the theorems of Rolewicz and Neerven type for uniform exponential stability of evolution families. We obtain necessary and sufficient conditions for uniform exponential stability of evolution families, generalizing a stability theorem due to Rolewicz and we present a new proof for the Rolewicz theorem, based on the theory of Banach function spaces. Finally, we apply our results and we deduce a generalization for a classical stability theorem due to Przyluski and Rolewicz.

Acknowledgements

The author would like to thank the referees for their suggestions and comments.

Notes

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