Hyers–Ulam Stability for a Type of Discrete Hill Equation

We establish the Hyers–Ulam stability of a second-order linear Hill-type h -difference equation with a periodic coefficient. Using results from first-order h -difference equations with periodic coefficient of arbitrary order, both homogeneous and non-homogeneous, we also establish a Hyers–Ulam stability constant. Several interesting examples are provided. As a powerful application, we use the main result to prove the Hyers–Ulam stability of a certain third-order h -difference equation with periodic coefficients of one form.