Hyers-Ulam stability of first-order nonhomogeneous linear difference equations with a constant stepsize

The present paper deals with Hyers-Ulam stability of the first-order linear difference equation Δhx(t)−ax(t)=f(t) on hZ, where Δhx(t)=(x(t+h)−x(t))/h and hZ={hk|k∈Z} for the constant stepsize h > 0; a is a real number; f(t) is a real-valued function on hZ. The main purpose of this paper is to find the best HUS constant on hZ. Several relationships between solutions of two different perturbed difference equations are also given.