Hyers--Ulam Stability for Discrete Time Scale with Two Step Sizes

We clarify the Hyers–Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, in the case of a specific time scale with two alternating step sizes, where the exponential function changes sign. In particular, in the case of HUS, we discuss the HUS constant, and whether a minimal constant can be found.