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<p>In this paper, we determine the best Ulam constant for <i>p</i>-order quaternion linear difference equations. Firstly, we use the constant variation formula to derive the general solution of this equation with <i>p</i> distinct characteristic roots. Secondly, we present the Hyers-Ulam stability of such an equation when the modulus of the characteristic roots is not equal to 1. Finally, the best Ulam constant of this equation is determined when the modulus of the characteristic roots is greater than 1. Additionally, as corollaries of our main results, we obtain the best Ulam constants for the first-order and second-order cases, as well as for the complex linear difference equations. Examples are given to illustrate the obtained results.</p>

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Best Ulam constant for p-order quaternion linear difference equation

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • Yuqun Zou,
  • JinRong Wang

摘要

In this paper, we determine the best Ulam constant for p-order quaternion linear difference equations. Firstly, we use the constant variation formula to derive the general solution of this equation with p distinct characteristic roots. Secondly, we present the Hyers-Ulam stability of such an equation when the modulus of the characteristic roots is not equal to 1. Finally, the best Ulam constant of this equation is determined when the modulus of the characteristic roots is greater than 1. Additionally, as corollaries of our main results, we obtain the best Ulam constants for the first-order and second-order cases, as well as for the complex linear difference equations. Examples are given to illustrate the obtained results.