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A FIXED POINT APPROACH TO THE STABILITY OF AN ADDITIVE-CUBIC-QUARTIC FUNCTIONAL EQUATION

  • Lee, Yang-Hi (Department of Mathematics Education, Gongju National University of Education)
  • Received : 2019.06.12
  • Accepted : 2019.11.19
  • Published : 2019.11.30

Abstract

In this paper, we investigate the stability of an additive-cubic-quartic functional equation f(x + 2y) - 4f(x + y) + 6f(x) - 4f(x - y) + f(x - 2y) - 12f(y) - 12f(-y) = 0 by applying the fixed point theory in the sense of L. Cădariu and V. Radu.

Keywords

References

  1. T. Aoki: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Japan 2 (1950), 64-66. https://doi.org/10.2969/jmsj/00210064
  2. J. Baker: A general functional equation and its stability. Proc. Natl. Acad. Sci. 133 (2005), no. 6, 1657-1664.
  3. L. Cadariu & V. Radu: Fixed points and the stability of Jensen's functional equation. J. Inequal. Pure Appl. Math. 4 (2003), no. 1, Art. 4.
  4. L. Cadariu & V. Radu: Fixed points and the stability of quadratic functional equations. An. Univ. Timisoara Ser. Mat.-Inform. 41 (2003), 25-48.
  5. L. Cadariu & V. Radu: On the stability of the Cauchy functional equation: a fixed point approach in Iteration Theory. Grazer Mathematische Berichte, Karl-Franzens-Universitaet, Graz, Graz, Austria 346 (2004), 43-52.
  6. Y.J. Cho & R. Saadati: Lattictic non-archimedean random stability of ACQ functional equation. Adv. Differ. Equ. 2011, no. 1, 31. https://doi.org/10.1186/s13662-020-2504-7
  7. J.B. Diaz & B. Margolis: A fixed point theorem of the alternative for contractions on a generalized complete metric space. Bull. Amer. Math. Soc. 74 (1968), 305-309. https://doi.org/10.1090/S0002-9904-1968-11933-0
  8. 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
  9. M.E. Gordji, Y.J. Cho, H. Khodaei & M. Ghanifard: Solutions and stability of generalized mixedtType QCA-functional equations in random normed spaces. Annals of the Alexandru Ioan Cuza University-Mathematics 59 (2013), no. 2, 299-320. https://doi.org/10.2478/v10157-012-0047-2
  10. 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.
  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. Y.-H. Lee & S.-M. Jung: Generalized Hyers-Ulam stability of some cubic-quadratic-additive type functional equations. (2000), submitted.
  13. 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.
  14. 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
  15. I.A. Rus: Principles and Applications of Fixed Point Theory. Ed. Dacia, Cluj-Napoca 1979(in Romanian).
  16. R. Saadati, M.M. Zohdi & S.M. Vaezpour: Nonlinear L-random stability of an ACQ functional equation. J. Inequal. Appl. 2011 Article ID 194394.
  17. S.M. Ulam: A Collection of Mathematical Problems. Interscience, New York, 1960.
  18. 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.