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

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Abstract

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.

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Acknowledgements

The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from the editor too.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    Maosong Yang & JinRong Wang

  2. Supercomputing Algorithm and Application Laboratory of Guizhou University and Gui’an Scientific Innovation Company, Guizhou University, Guiyang, 550025, Guizhou, China

    Maosong Yang & JinRong Wang

  3. School of Information Engineering, Guizhou Open University, Guiyang, 550023, Guizhou, China

    Maosong Yang

  4. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  5. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

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  1. Maosong Yang
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  2. Michal Fečkan
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This work is partially supported by the National Natural Science Foundation of China (12161015), Guizhou Provincial Basic Research Program (Natural Science) [2023]034, and Qian Ke He Ping Tai Ren Cai-YSZ[2022]002, and the Slovak Grant Agency VEGA No. 2/0127/20 and No. 1/0084/23.

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Yang, M., Fečkan, M. & Wang, J. Ulam’s Type Stability of Delayed Discrete System with Second-Order Differences. Qual. Theory Dyn. Syst. 23, 11 (2024). https://doi.org/10.1007/s12346-023-00868-y

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