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.
