On Uniform h-Stability of Evolution Operators in Banach Spaces

Abstract

The paper treats the general concept of uniform h-stability, as a generalization of uniform exponential stability
for evolution operators in Banach spaces.
The main aim is to give necessary and sucient conditions of Datko-type and Barbashin-type for this property and
also criterias for uniform h-stability using Lyapunov functions. As particular cases, we obtain the results for uniform
exponential stability.