Hyers–Ulam Stability of Linear Recurrence with Constant Coefficients Over the Quaternion Skew Yield

In this paper, we discuss the Hyers–Ulam stability of the linear recurrence over the quaternion skew yield by considering the associated first-order matrix difference equations in complex Banach space. Firstly, we show the Hyers–Ulam stability result for the first-order quaternion-valued linear recurrence. Secondly, we give the sufficient conditions to present the Hyers–Ulam stability of the second-order quaternion-valued linear recurrence. Further, we extend to derive the general result for the higher-order quaternion-valued linear recurrence. Finally, examples are presented to illustrate the theoretical results.