Best Hyers--Ulam stability constants on a time scale with discrete core and continuous periphery,

D. R. Anderson and M. Onitsuka

Consider a time scale consisting of a discrete core with uniform step
size, augmented with a continuous-interval periphery. On this time scale, we
determine the best constants for the Hyers–Ulam stability of a first-order dynamic
equation with complex constant coefficient, based on the placement of the complex
coefficient in the complex plane, with respect to the imaginary axis and the Hilger
circle. These best constants are then related to known results for the special cases of
completely continuous and uniformly discrete time scales.

Nonlinear Analysis, Differential Equations and Applications, Springer Optimization and Its Applications

Springer

173

17

37

https://doi.org/10.1007/978-3-030-72563-1_2