Abstract
First, we prove that the best (minimum) constant for Hyers–Ulam stability of first-order linear h-difference equations with a complex constant coefficient is the reciprocal of the absolute value of the Hilger real part of that coefficient; if the coefficient lies on the Hilger imaginary circle, then the equation is unstable in the Hyers–Ulam sense. Second, using this best constant from the first-order complex coefficient case, we determine the best constant for Hyers–Ulam stability of second-order linear h-difference equations with constant real coefficients. The second-order equation also is Hyers–Ulam stable if and only if the values of the characteristic equation do not intersect the Hilger imaginary circle.
Published Version
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