Korean Journal of Mathematics

  • 제28권2호
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  • Pages.159-168
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  • 2020
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC-CUBIC-QUARTIC FUNCTIONAL EQUATION

  • Lee, Yang-Hi (Department of Mathematics Education Gongju National University of Education)
  • 투고 : 2019.04.10
  • 심사 : 2020.03.09
  • 발행 : 2020.06.30
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초록

In this paper, we investigate Hyers-Ulam-Rassias stability of a functional equation f(x + ky) + f(x - ky) - k2f(x + y) - k2f(x - y) + 2(k2 - 1)f(x) + (k2 + k3)f(y) + (k2 - k3)f(-y) - 2f(ky) = 0.

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참고문헌

  1. J. Baker, A general functional equation and its stability, Proc. Natl. Acad. Sci. 133 (6) (2005), 1657-1664.
  2. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211
  3. D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  4. M. E. Gordji, H. Khodaei, and R. Khodabakhsh, General quartic-cubic-quadratic functional equation in non-Archimedean normed spaces, U.P.B. Sci. Bull. Series A 72 (3) (2010), 69-84.
  5. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  6. S.M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.