DOI QR코드

DOI QR Code

ON THE STABILITY OF A MIXED TYPE QUADRATIC AND CUBIC FUNCTIONAL EQUATION

  • Lee, Chang-Ju (Department of Mathematics Education, Gongju National University of Education) ;
  • Lee, Yang-Hi (Department of Mathematics Education, Gongju National University of Education)
  • Received : 2012.08.07
  • Accepted : 2012.10.16
  • Published : 2012.11.30

Abstract

In this paper, we investigate a fuzzy version of stability for the functional equation $$f(x+2y)-3f(x+y)+3f(x)-f(x-y)-3f(y)+3f(-y)=0$$ in the sense of M. Mirmostafaee and M. S. Moslehian.

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. T. Bag & S.K. Samanta: Finite dimensional fuzzy normed linear spaces. J. fuzzy Math. 11 (2003), no. 3, 687-705.
  3. S.C. Cheng & J.N. Mordeson: Fuzzy linear operator and fuzzy normed linear spaces. Bull. Calcutta Math. Soc. 86 (1994), 429-436.
  4. 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
  5. 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
  6. A. K. Katsaras: Fuzzy topological vector spaces II. Fuzzy Sets and Systems 12 (1984), 143-154. https://doi.org/10.1016/0165-0114(84)90034-4
  7. I. Kramosil & J. Michalek: Fuzzy metric and statistical metric spaces. Kybernetica 11 (1975), 326-334.
  8. Y.-H. Lee: On the stability of the monomial functional equation. Bull. Korean Math. Soc. 45 (2008), 397-403. https://doi.org/10.4134/BKMS.2008.45.2.397
  9. Y.-H. Lee & 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
  10. A. K. Mirmostafaee & M. S. Moslehian: Fuzzy versions of Hyers-Ulam-Rassias theorem. Fuzzy Sets and Systems 159 (2008), 720-729. https://doi.org/10.1016/j.fss.2007.09.016
  11. M. Mursaleen & S.A. Mohiuddine: On stability of a cubic functional equation in intu- itionistic fuzzy normed spaces. Chaos, Solitons & Fractals 42 (2009), 2997-3005. https://doi.org/10.1016/j.chaos.2009.04.041
  12. 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
  13. W. Towanlong & P. Nakmahachalasint: A mixed-type quadratic and cubic functional equation and its stability. Thai Journal of Mathematics Special Issue (Annual Meeting in Mathematics) (2010), 61-71.
  14. S.M. Ulam: A Collection of Mathematical Problems. Interscience, New York (1960).