Best Hyers–Ulam Stability Constants on a Time Scale with Discrete Core and Continuous Periphery

Douglas R Anderson,Masakazu Onitsuka

doi:10.1007/978-3-030-72563-1_2

Best Hyers–Ulam Stability Constants on a Time Scale with Discrete Core and Continuous Periphery

Douglas R Anderson, Masakazu Onitsuka

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

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Publication Date: Jan 1, 2021

Affiliation: Concordia College - Minnesota, Okayama University of Science

#Hyers Ulam Stability Constants #Uniform Step Size + Show 8 more

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Abstract

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.

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