한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제26권4호
  • /
  • Pages.247-254
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  • 2019
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  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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ON THE HYERS-ULAM-RASSIAS STABILITY OF AN ADDITIVE-CUBIC-QUARTIC FUNCTIONAL EQUATION

  • Lee, Yang-Hi (Department of Mathematics Education, Gongju National University of Education)
  • 투고 : 2019.03.28
  • 심사 : 2019.11.19
  • 발행 : 2019.11.30
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초록

In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation f(x + ky) - k2f(x + y) + 2(k2 - 1)f(x) - k2f(x - y) + f(x - ky) - k2(k2 - 1)(f(y) + f(-y)) = 0, where k is a fixed real number with |k| ≠ 0, 1.

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참고문헌

  1. J. Baker: A general functional equation and its stability. Proc. Natl. Acad. Sci. 133 (2005), no. 6, 1657-1664.
  2. Y.J. Cho & R. Saadati: Lattictic non-archimedean random stability of ACQ functional equation. Adv. Differ. Equ. 2011(1), 31. https://doi.org/10.1186/1687-1847-2011-31
  3. 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
  4. M.E. Gordji, Y.J. Cho, H. Khodaei & M. Ghanifard: Solutions and stability of generalized mixed type QCA-functional equations in random normed spaces. Annals of the Alexandru Ioan Cuza University-Mathematics 59 (2013), 299-320. https://doi.org/10.2478/v10157-012-0047-2
  5. M.E. Gordji, S.K. Gharetapeh, C. Park & S. Zolfaghri: Stability of an additive-cubic-quartic functional equation. Adv. Differ. Equ. 2009 Article ID 395693.
  6. D.H. Hyers: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  7. J.M. Rassias, M. Arunkumar, E. Sathya & N. Mahesh Kumar: Solution and stability of an ACQ functional equation in generalized 2-normed spaces. Intern. J. Fuzzy Mathematical Archive 7 (2015), 213-224.
  8. 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
  9. R. Saadati, M.M. Zohdi & S.M. Vaezpour: Nonlinear L-random stability of an ACQ functional equation. J. Inequal. Appl. 2011 Article ID 194394.
  10. S.M. Ulam: A Collection of Mathematical Problems. Interscience, New York, 1960.
  11. Z. Wang, X. Li & Th.M. Rassias: Stability of an additive-cubic-quartic functional equation in multi-Banach spaces. Abstr. Appl. Anal. 2011 Article ID 536520.