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

TitleThe conditions of Hyers—Ulam—Rassias-stability of a set of equations
Publication TypeJournal Article
Year of Publication2017
AuthorsMartynyuk, AA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2017.08.011
Issue8
SectionMathematics
Pagination11-16
Date Published8/2017
LanguageRussian
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.

KeywordsHyers—Ulam—Rassias-stability, set of equations with causal operators, set of regularized equations
References: 
  1. 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
  2. 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
  3. Ulam, S. M. (1960). A Collection of the Mathematical Problems. New York: Interscience.
  4. Laksmikantham, V., Bhaskar, T. G. & Devi, J. V. (2006). Theory of Set Differential Equations in Metric Spaces. Cambridge: Cambridge Scientific Publishers.
  5. Martynyuk, A. A. & Martynyuk-Chernienko, Yu. A. (2012). Uncertain Dynamical Systems: Stability and Motion Control. Boca Raton, London, New York: CRC Press.
  6. Rus, I. A. (2010). Ulam stabilities of ordinary differential equations in a Banach space. Carpathian J. Math., 26, No. 1, pp. 103-107.
  7. Corduneanu, C., Li, Y. & Mahdavi, M. (2016). Functional Differential Equations: Advances and Applications. New York: Wiley. https://doi.org/10.1002/9781119189503