ON (h, k)-EXPONENTIAL STABILITY OF EVOLUTION OPERATORS IN BANACH SPACES

The paper considers a general concept of stability for evolution operators in Banach spaces, the so-called (h, k)-stability. This concept includes a great variety of uniform and nonuniform asymptotical behaviors, among them uniform exponential stability, exponential stability in the sense Barreira-Valls and non-uniform exponential stability. We present some integral characterizations and relations between these concepts. The results obtained are generalizations of some well-known theorems proved by Datko, Buse and Megan.