East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

HYERS-ULAM-RASSIAS STABILITY OF AN ADDITIVE-QUARTIC, A QUADRATIC-QUARTIC, AND A CUBIC-QUARTIC FUNCTIONAL EQUATION

  • Jin, Sun-Sook (Department of Mathematics Education, Gongju National University of Education) ;
  • Lee, Yang-Hi (Department of Mathematics Education, Gongju National University of Education)
  • Received : 2019.11.07
  • Accepted : 2020.01.02
  • Published : 2020.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we investigate Hyers-Ulam-Rassias stability of an additive-quartic functional equation, of a quadratic-quartic functional equation, and of a cubic-quartic functional equation.

Keywords

References

  1. S. Abbaszadeh, Intutionistic fuzzy stability of a quadratic and quartic functional equation, Int. J. Nonlinear Anal. Appl. 1 (2010), 100-124.
  2. J. Baker, A general functional equation and its stability, Proc. Natl. Acad. Sci. 133(6) (2005), 1657-1664.
  3. A. Bodaghi, Stability of a mixed type additive and quartic functional equation, Filomat, 28(8) (2014) 1629-1640. https://doi.org/10.2298/FIL1408629B
  4. A. Bodaghi, Approximate mixed type additive and quartic functional equation, Bol. Soc. Paran. Mat. 35(1) (2017), 43-56. https://doi.org/10.5269/bspm.v35i1.29014
  5. 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
  6. M. E. Gordji, Stability of a functional equation deriving from quartic and additive functions, arXiv preprint arXiv:0812.5025 (2008).
  7. M. E. Gordji, S. Abbaszadeh, and C. Park, On the stability of a generalized quadratic and quartic type functional equation in quasi-Banach spaces, J. Inequal. Appl. 2009 Article ID 153084.
  8. M. E. Gordji, A. Ebadian, and S. Zolfaghari, Stability of a functional equation deriving from cubic and quartic functions, Abstr. Appl. Anal. 2008 Article ID 801904.
  9. M. E. Gordji, M. B. Savadkouhi, Stability of a mixed type cubic-quartic functional equation in non-archimedean spaces, Appl. Math. Lett. 23 (2010), 1198-1202. https://doi.org/10.1016/j.aml.2010.05.011
  10. M. E. Gordji, M. B. Savadkouhi, and C. Park, Quadratic-quartic functional equations in RN-spaces, J. Inequal. Appl. 2009 Article ID 868423.
  11. 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
  12. S.-Y. Jang, C.-K. Park, and D. Y. Shin, Fuzzy stability of a cubic-quartic functional equation: A fixed point approach, Bull. Korean Math. Soc. 48 (2011), 491-503. https://doi.org/10.4134/BKMS.2011.48.3.491
  13. H.-M. Kim, On the stability problem for a mixed type of quartic and quadratic functional equation, J. Math. Anal. Appl. 324 (2006), 358-372. https://doi.org/10.1016/j.jmaa.2005.11.053
  14. J.-R. Lee, C.-K. Park, Y.-J. Cho and D.-Y. Shin, Orthogonal stability of a cubic-quartic functional equation in non-archimedean spaces, J. Comput. Anal. Appl. 15 (2013), 572-583.
  15. C.-K. Park, Orthogonal stability of a cubic-quartic functional equation, Journal of Nonlinear Sciences & Applications (JNSA) 5 (2012), 28-36. https://doi.org/10.22436/jnsa.005.01.04
  16. 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
  17. S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.
  18. Z. Wang and P. K. Sahoo, Stability of the generalized quadratic and quartic type functional equation in non-archimedean fuzzy normed spaces, J. Appl. Anal. Comput. 6 (2016), 917-938.
  19. T. Z. Xu, J. M. Rassias, and W. X. Xu, A generalized mixed quadratic-quartic functional equation, Bull. Malays. Math. Sci. Soc. 35(3) (2012), 633-649.
  20. X. Zhao, X. Yang, and C. T. Pang, Solution and stability of a general mixed type cubic and quartic functional equation, J. Funct. Spaces Appl. 2013 Article ID 673810.