DOI QR코드

DOI QR Code

ON THE HYERS-ULAM-RASSIAS STABILITY OF AN ADDITIVE-QUADRATIC-CUBIC FUNCTIONAL EQUATION

  • Lee, Yang-Hi (Department of Mathematics Education Gongju National University of Education)
  • Received : 2019.03.13
  • Accepted : 2019.06.21
  • Published : 2019.08.15

Abstract

In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation $$f(x+ky)-{\frac{k^2+k}{2}}f(x+y)+(k^2-1)f(x)-{\frac{k^2-k}{2}}f(x-y)\\{\hfill{67}}-f(ky)+{\frac{k^2+k}{2}}f(y)+{\frac{k^2-k}{2}}f(-y)=0.$$

References

  1. J. Baker, A general functional equation and its stability, Proc. Natl. Acad. Sci., 133 (2005), no. 6, 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.
  3. M. E. Gordji, M. Ghanifard, H. Khodaei, and C. Park, Fixed points and the random stability of a mixed type cubic, quadratic and additive functional equation, J. Comput. Anal. Appl., 15 (2013), 612-621.
  4. M. E. Gordji, S. K. Gharetapeh, J. M. Rassias, and S. Zolfaghari, Solution and stability of a mixed type additive, quadratic, and cubic Functional Equation, Adv. Difference Equ. 2009 Article ID 826130, 17 pages.
  5. M. E. Gordji, M. Kamyar, H. Khodaei, D. Y. Shin and C. Park, Fuzzy stability of generalized mixed type cubic, quadratic, and additive functional equation, J. Inequal. Appl., 2011, 2011:95, 22 pages.
  6. M. E. Gordji and H. Khodaie, Solution and stability of generalized mixed type cubic, quadratic and additive functional equation in quasi-Banach spaces, Nonlinear Anal., 71 (2009), 5629-5643.
  7. M. E. Gordji and M. B. Savadkouhi, Stability of a mixed type additive, quadratic, and cubic functional equation in random normed spaces, Filomat, 25 (2011), 43-54.
  8. M. E. Gordji, M. B. Savadkouhi, and Th. M. Rassias, Stability of generalized mixed type additive-quadratic-cubic functional equation in non-Archimedean spaces, arXiv preprint arXiv:0909.5692, (2009).
  9. D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A., 27 (1941), 222-224.
  10. K.-W. Jun and H.-M. Kim, On the Hyers-Ulam-Rassias stability of a general cubic functional equation, Math. Inequal. Appl., 6 (2003), 289-302.
  11. Y.-H. Lee, On the generalized Hyers-Ulam stability of the generalized polynomial function of degree 3, Tamsui Oxf. J. Math. Sci., 24 (2008), no. 4, 429-444.
  12. C. K. Park, A fixed point approach to the fuzzy stability of an additive-quadratic-cubic functional equation, Fixed Point Theory and Applications, 2009 (2009), Article ID 918785, 24 pages.
  13. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.
  14. S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.