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

In: Nonlinear Analysis, Differential Equations, and Applications

Author

Listed:
  • Douglas R. Anderson

    (Department of Mathematics)

  • Masakazu Onitsuka

    (Department of Applied Mathematics)

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.

Suggested Citation

  • Douglas R. Anderson & Masakazu Onitsuka, 2021. "Best Hyers–Ulam Stability Constants on a Time Scale with Discrete Core and Continuous Periphery," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Nonlinear Analysis, Differential Equations, and Applications, pages 17-37, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-72563-1_2
    DOI: 10.1007/978-3-030-72563-1_2
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