DOI QR코드

DOI QR Code

ON THE STABILITY OF THE GENERAL SEXTIC FUNCTIONAL EQUATION

  • Chang, Ick-Soon (Department of Mathematics Chungnam National University) ;
  • Lee, Yang-Hi (Department of Mathematics Education Gongju National University of Education) ;
  • Roh, Jaiok (Ilsong College of Liberal Arts Hallym University)
  • Received : 2021.07.08
  • Accepted : 2021.08.07
  • Published : 2021.08.15

Abstract

The general sextic functional equation is a generalization of many functional equations such as the additive functional equation, the quadratic functional equation, the cubic functional equation, the quartic functional equation and the quintic functional equation. In this paper, motivating the method of Găvruta [J. Math. Anal. Appl., 184 (1994), 431-436], we will investigate the stability of the general sextic functional equation.

Keywords

Acknowledgement

This work was partially supported by Data Science Convergence Research Center of Hallym University.

References

  1. S. Alshybani, S. M. Vaezpour and R. Saadati, Generalized Hyers-Ulam stability of sextic functional equation in random normed spaces, J. Comput. Anal. Appl., 24 (2018), no. 2, 370-381.
  2. S. Alshybani, S. M. Vaezpour and R. Saadati, Stability of the sextic functional equation in various spaces, J. Inequal. Spec. Funct., 9 (2018), no. 4, 8-27.
  3. J. Baker, A general functional equation and its stability, Proc. Natl. Acad. Sci., 133 (2005), no. 6, 1657-1664.
  4. Y. J. Cho, M. B. Ghaemi, M. Choubin and M. E. Gordji, On the Hyers-Ulam stability of sextic functional equations in β-homogeneous probabilistic modular spaces, Math. Inequal. Appl., 16 (2013), no. 4, 1097-1114.
  5. I. I. EL-Fassi, New stability results for the radical sextic functional equation related to quadratic mappings in (2, β)-Banach spaces, J. Fixed Point Theory Appl., 20 (2018), 138, 1-17. https://doi.org/10.1007/s11784-018-0489-6
  6. Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci., 14 (1991), no. 3, 431-434. https://doi.org/10.1155/S016117129100056X
  7. 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
  8. 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
  9. G. Isac and T. M. Rassias, On the Hyers-Ulam stability of ψ-additive mappings, J. Approx. Theory, 72 (1993), 131-137. https://doi.org/10.1006/jath.1993.1010
  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. S.-M. Jung, On the Hyers-Ulam-Rassias stability of approximately additive map-pings, J . Math. Anal. Appl., 204 (1996), 221-226. https://doi.org/10.1006/jmaa.1996.0433
  12. J. Roh, Y. H. Lee and S. -M. Jung The Stability of a General Sextic Functional Equation by Fixed Point Theory, J. Funct. Spaces, 2020 (2020), 1-8. https://doi.org/10.1155/2020/4016386
  13. 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.
  14. Y.-H. Lee, On the Hyers-Ulam-Rassias stability of the generalized polynomial function of degree 2, J. Chungcheong Math. Soc., 22 (2009), no.2, 201-209.
  15. Y.-H. Lee, Stability of a monomial functional equation on a restricted domain, Mathematics, 5 (2017), 53. https://doi.org/10.3390/math5040053
  16. Y.-H. Lee, On the Hyers-Ulam-Rassias stability of a general quartic functional equation, East Asian Math. J., 35 (2019), no. 3, 351-356. https://doi.org/10.7858/EAMJ.2019.031
  17. Y.-H. Lee, On the Hyers-Ulam-Rassias stability of a general quintic functional equation and a general sextic functional equation, Mathematics, 7 (2019), 510. https://doi.org/10.3390/math7060510
  18. Y.-H. Lee and K. W. Jun, On the stability of approximately additive mappings, Proc. Amer. Math. Soc., (2000), 1361-1369.
  19. A. Najati and C. Park, Fixed Points and Stability of a Generalized Quadratic Functional Equation J. Inequal. Appl., 2009(2009), Article ID 193035, 19 pages.
  20. 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
  21. T. Xu, J. Rassias, M. Rassias and W. Xu, A fixed point approach to the stability of quintic and sextic functional equations in quasi-β-normed spaces, J. Inequal. Appl., 2010 (2010), Article ID 423231, 23 pages.
  22. T. Xu, J. Rassias, M. Rassias and W. Xu, Stability of quintic and sextic functional equations in non-archimedean fuzzy normed spaces, Eighth International Conference on Fuzzy Systems and Knowledge Discovery, 2011.
  23. K. Ravi and S. Sabarinathan, Generalized Hyers-Ulam stability of a sextic functional equation in paranormed spaces, International Journal of Mathematics Trends and Technology, 9 (2014), no. 1, 61-69. https://doi.org/10.14445/22315373/IJMTT-V9P506
  24. S. Ostadbashi and M. Soleimaninia, On the stability of the orthogonal pexiderized quartic functional equations, Nonlinear Funct. Anal. Appl., 20 (2015), no. 4, 539-549.
  25. S.M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.