The conditions of Hyers—Ulam—Rassias-stability of a set of equations

Authors

  • A.A. Martynyuk S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kiev

DOI:

https://doi.org/10.15407/dopovidi2017.08.011

Keywords:

Hyers—Ulam—Rassias-stability, set of equations with causal operators, set of regularized equations

Abstract

For a set of regularized equations and a set of equations with causal operators, the sufficient conditions of Hyers—Ulam—Rassias-stability are obtained.

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References

Hyers, D. H. (1941). On the stability of the linear functional equation. Proc. Natl. Acad. Sci. U. S. A., 27, pp. 222-224. https://doi.org/10.1073/pnas.27.4.222

Rassias, Th. M. (1978). Functional Equations, Inequalities and Applications, Proc. Amer. Math. Soc., 72, pp. 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1

Ulam, S. M. (1960). A Collection of the Mathematical Problems. New York: Interscience.

Laksmikantham, V., Bhaskar, T. G. & Devi, J. V. (2006). Theory of Set Differential Equations in Metric Spaces. Cambridge: Cambridge Scientific Publishers.

Martynyuk, A. A. & Martynyuk-Chernienko, Yu. A. (2012). Uncertain Dynamical Systems: Stability and Motion Control. Boca Raton, London, New York: CRC Press.

Rus, I. A. (2010). Ulam stabilities of ordinary differential equations in a Banach space. Carpathian J. Math., 26, No. 1, pp. 103-107.

Corduneanu, C., Li, Y. & Mahdavi, M. (2016). Functional Differential Equations: Advances and Applications. New York: Wiley. https://doi.org/10.1002/9781119189503

Published

15.09.2024

How to Cite

Martynyuk, A. (2024). The conditions of Hyers—Ulam—Rassias-stability of a set of equations . Reports of the National Academy of Sciences of Ukraine, (8), 11–16. https://doi.org/10.15407/dopovidi2017.08.011

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