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Hyers–Ulam stability of first-order nonhomogeneous linear difference equations with a constant stepsize

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  • Onitsuka, Masakazu

Abstract

The present paper deals with Hyers–Ulam stability of the first-order linear difference equation Δhx(t)−ax(t)=f(t) on hZ, where Δhx(t)=(x(t+h)−x(t))/h and hZ={hk|k∈Z} for the constant stepsize h > 0; a is a real number; f(t) is a real-valued function on hZ. The main purpose of this paper is to find the best HUS constant on hZ. Several relationships between solutions of two different perturbed difference equations are also given.

Suggested Citation

  • Onitsuka, Masakazu, 2018. "Hyers–Ulam stability of first-order nonhomogeneous linear difference equations with a constant stepsize," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 143-151.
    • Handle: RePEc:eee:apmaco:v:330:y:2018:i:c:p:143-151
    DOI: 10.1016/j.amc.2018.02.036
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    References listed on IDEAS

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    1. Zada, Akbar & Shah, Omar & Shah, Rahim, 2015. "Hyers–Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 512-518.
    2. Youssef Manar & Elhoucien Elqorachi & Themistocles M. Rassias, 2014. "On the Generalized Hyers–Ulam Stability of the Pexider Equation on Restricted Domains," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Handbook of Functional Equations, edition 127, pages 279-299, Springer.
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    Cited by:

    1. Anderson, Douglas R. & Onitsuka, Masakazu, 2019. "Hyers–Ulam stability for a discrete time scale with two step sizes," Applied Mathematics and Computation, Elsevier, vol. 344, pages 128-140.

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