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

Yuqun Zo, Michal Feckan, JinRong Wang

• 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.