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We establish the best (minimum) constant for Ulam stability of first-orderlinear $h$-difference equations with a periodic coefficient. First, we showUlam stability and find the Ulam stability constant for a first-order linearequation with a period-two coefficient, and give several examples. In the lastsection we prove Ulam stability for a periodic coefficient function ofarbitrary finite period. Results on the associated first-order perturbed linearequation with periodic coefficient are also included.

Best constant for Ulam stability of first-order h-difference equations with periodic coefficient