Abstract
In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: \( x(n+1) = A(n)x(n) \) and \( x_{i}(n+1)=\sum _{j=1}^{m}a_{ij}(n)g_{j}(x_{j}(n)) \quad \text{ for } \quad 1 \le i \le m \), respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.
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Hamaya, Y. (2019). Existence and Stability Properties of Almost Periodic Solutions in Discrete Almost Periodic Systems. In: Elaydi, S., Pötzsche, C., Sasu, A. (eds) Difference Equations, Discrete Dynamical Systems and Applications. ICDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 287. Springer, Cham. https://doi.org/10.1007/978-3-030-20016-9_11
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