Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A FIXED POINT APPROACH TO THE STABILITY OF AN ADDITIVE-QUADRATIC-QUARTIC FUNCTIONAL EQUATION

  • Lee, Yang-Hi (Department of Mathematics Education Gongju National University of Education)
  • Received : 2019.10.02
  • Accepted : 2020.01.21
  • Published : 2020.02.15
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Abstract

In this paper, we investigate the stability of a functional equation f(x + 3y) - 5f(x + 2y) + 10f(x + y) - 8f(x) + 5f(x - y) - f(x - 2y) - 2f(-x) - f(2x) + f(-2x) = 0 by using the fixed point theory in the sense of L. Cǎdariu and V. Radu.

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References

  1. J. Baker, A general functional equation and its stability, Proc. Amer. Math. Soc., 133 (2005), no. 6, 1657-1664. https://doi.org/10.1090/S0002-9939-05-07841-X
  2. L. Cadariu and V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math., 4 (2003), no. 1, Art. 4.
  3. L. Cadariu and V. Radu, Fixed points and the stability of quadratic functional equations, An. Univ. Timisoara Ser. Mat.-Inform., 41 (2003), 25-48.
  4. L. Cadariu and 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.
  5. J. B. Diaz and 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
  6. 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
  7. A. K. Hassan, J. R. Lee, and C. Park, Non-Archimedean stability of an AQQ functional equation, J. Comput. Anal. Appl., 14 (2012), 211-227.
  8. 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
  9. S.-S. Jin and Y.-H. Lee, A fixed point approach to the stability of the quadratic and quartic type functional equation, J. Chungcheong Math. Soc., 32 (2019), 337-347. https://doi.org/10.14403/jcms.2019.32.3.337
  10. Y.-H. Lee, A fixed point approach to the stability of a quadratic-cubic-quartic functional equation, East Asian Math. J., 35 (2019), 559-568. https://doi.org/10.7858/EAMJ.2019.044
  11. Y.-H. Lee, A fixed point approach to the stability of an additive-cubic-quartic functional equation, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., 26 (2019), 267-276.
  12. Y.-H. Lee, A fixed point approach to the stability of a quadratic-cubic functional equation, Korean J. Math., 27 (2019), 343-355. https://doi.org/10.11568/KJM.2019.27.2.343
  13. Y. H. Lee and K. W. Jun, On the stability of approximately additive mappings, Proc. Amer. Math. Soc., 128 (2000), 1361-1369. https://doi.org/10.1090/S0002-9939-99-05156-4
  14. Y.-H. Lee and S.-M. Jung, A fixed point approach to the stability of an additive-quadratic-cubic-quartic functional equation, J. Function Spaces, (2016), Art. ID 8746728, 7 pages.
  15. Y.-H. Lee and S.-M. Jung, A fixed point approach to the stability of a general quartic functional equation, J. Math. Computer Sci., 20 (2020), 207-215.
  16. M. Mohamadi, Y. J. Cho, C. Park, P. Vetro, and R. Saadati, Random stability of an additive-quadratic-quartic functional equation, J. Inequal. Appl., 2010 (2010), Art. ID 754210, 18 pages.
  17. C. Park, Fuzzy stability of an additive-quadratic-quartic functional equation, J. Inequal. Appl., 2010 (2010), Art. ID 253040, 22 pages
  18. 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
  19. I.A. Rus, Principles and Applications of Fixed Point Theory, Ed. Dacia, Cluj-Napoca, 1979 (in Romanian).
  20. S.M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.