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Absolute asymptotic stability of discrete linear inclusions. (English) Zbl 1081.39002
The authors study diverse stability concepts for discrete linear inclusions in Banach spaces. They establish the relations between absolute asymptotic stability, asymptotic stability, uniform asymptotic stability and uniform exponential stability. One of the main results states that for asymptotical compact discrete linear inclusions, the concepts of asymptotic stability and uniform exponential stability are equivalent.

39A11 Stability of difference equations (MSC2000)
34A60 Ordinary differential inclusions
34D20 Stability of solutions to ordinary differential equations
37C75 Stability theory for smooth dynamical systems
37B55 Topological dynamics of nonautonomous systems
39A12 Discrete version of topics in analysis