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Hyers–Ulam Stability of Linear Homogeneous Quaternion-Valued Difference Equations

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Abstract

In this paper, we consider the Hyers–Ulam stability of the first-order linear homogeneous quaternion matrix difference equation. Furthermore, we prove the Hyers-Ulam stability of the second-order linear homogeneous quaternion-valued forward and backward difference equation by converting them into the first-order quaternion matrix difference equation. Finally, some examples are given to support the 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.

Funding

This work is supported by the National Natural Science Foundation of China (12161015) and Guizhou Provincial Basic Research Program (Natural Science) [2023]034, and Introduced Talents Program of Guizhou University [(2022)50].

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guizhou University, Guiyang, 550025, Guizhou, China

    Jiangnan Wang, JinRong Wang & Rui Liu

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

    Jiangnan Wang, JinRong Wang & Rui Liu

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  1. Jiangnan Wang
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  2. JinRong Wang
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  3. Rui Liu
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Correspondence to JinRong Wang.

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Wang, J., Wang, J. & Liu, R. Hyers–Ulam Stability of Linear Homogeneous Quaternion-Valued Difference Equations. Qual. Theory Dyn. Syst. 22, 119 (2023). https://doi.org/10.1007/s12346-023-00818-8

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