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Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales

Anderson D. R., Onitsuka M.

Demonstratio Mathematica

2018

Vol. 51, nr 1

198--210

We establish the Hyers-Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, which include the continuous (step size zero) and the discrete (step size constant and nonzero) dynamic equations as important special cases. In particular, for certain parameter values in relation to the graininess of the time scale, we find the minimum HUS constants. A few nontrivial examples are provided. Moreover, an application to a perturbed linear dynamic equation is also included.