Abstract
Let q>1 be a fixed integer number. We prove that a discrete q-periodic evolution family on a complex Banach space is uniformly asymptotically stable, that is, U(m, n) → 0 in the norm of when (m − n) → ∞, if and only if for each and each x ∈ X one has In particular, we obtain the following result of Datko type. The family is uniformly asymptotically stable if and only if for each one has
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