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Hyers-Ulam Stability of the Delay Equation

Author

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  • Soon-Mo Jung
  • Janusz Brzdęk

Abstract

We investigate the approximate solutions of the delay differential equation with an initial condition, where and are real constants. We show that they can be “approximated†by solutions of the equation that are constant on the interval and, therefore, have quite simple forms. Our results correspond to the notion of stability introduced by Ulam and Hyers.

Suggested Citation

  • Soon-Mo Jung & Janusz Brzdęk, 2010. "Hyers-Ulam Stability of the Delay Equation," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-10, December.
    • Handle: RePEc:hin:jnlaaa:372176
    DOI: 10.1155/2010/372176
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    Cited by:

    1. Zada, Akbar & Ali, Wajid & Park, Choonkil, 2019. "Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall-Bellman-Bihari’s type," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 60-65.
    2. Daniela Marian, 2021. "Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations," Mathematics, MDPI, vol. 9(24), pages 1-15, December.

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