Best constant for Hyers-Ulam stability of two step sizes linear difference equations

D. R. Anderson and M. Onitsuka

This study deals with the Hyers–Ulam stability (HUS) for the first-order linear difference equations with two alternating step sizes, where the coefficient is allowed to be complex valued. In particular, it turns out that the best HUS constant can be determined by finding an explicit solution to the corresponding inhomogeneous linear equation. Special cases of these results validate previous literature in the field.

Journal of Mathematical Analysis and Applications

496

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