Ulam's Type Stability of Delayed Discrete System with Second-Order Differences

In this paper, the Ulam's type stability of delayed discrete systems with a second-order difference is investigated. Firstly, we introduce the Hyers-Ulam stability and Hyers-Ulam-Rassias stability concepts for delayed discrete systems with a second-order difference. Secondly, the uniqueness and existence of the solution of delayed nonlinear discrete systems is proved based on fixed point theory, and the Ulam's type stability results are presented with the help of the delayed discrete matrix function and discrete Gronwall inequality. Finally, two examples are presented to demonstrate the effectiveness of theoretical results.