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

Douglas R. Anderson () and Masakazu Onitsuka ()
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Douglas R. Anderson: Department of Mathematics
Masakazu Onitsuka: Department of Applied Mathematics

A chapter in Nonlinear Analysis, Differential Equations, and Applications, 2021, pp 17-37 from Springer

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-72563-1_2

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

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