Solvability and Hyers-Ulam Stability of Quaternion Difference Equations With Two-sided Coefficients

This paper delves into solvability and Hyers-Ulam stability of a class of quaternion difference equations with two-sided coefficients. Firstly, we obtain the general solutions and Hyers-Ulam stability of first-order two-sided coefficients quaternion difference equations by induction and the real representation of quaternions, respectively. Secondly, by using the complex representation of quaternions, we solve second-order quaternion difference equations with two-sided coefficients and provide the Hyers-Ulam stability results. Further, we generalize the second-order results to attain the general results of higher-order quaternion difference equations with two-sided coefficients. Finally, examples are given to demonstrate the obtained results.