Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

STABILITY OF MULTIPLICATIVE INVERSE FUNCTIONAL EQUATIONS IN THREE VARIABLES

  • Received : 2011.11.15
  • Accepted : 2011.12.07
  • Published : 2012.03.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we prove stabilities of multiplicative functional equations in three variables such as $r(\frac{x+y+z}{3})-r(x+y+z)$=$\frac{2r(\frac{x+y}{2})r(\frac{y+z}{2})r(\frac{z+x}{2})}{r(\frac{x+y}{2})r(\frac{y+z}{2})+r(\frac{y+z}{2})r(\frac{z+x}{2})+r(\frac{z+x}{2})r(\frac{x+y}{2})}$ and $r(\frac{x+y+z}{3})+r(x+y+z)$=$\frac{4r(\frac{x+y}{2})r(\frac{y+z}{2})r(\frac{z+x}{2})}{r(\frac{x+y}{2})r(\frac{y+z}{2})+r(\frac{y+z}{2})r(\frac{z+x}{2})+r(\frac{z+x}{2})r(\frac{x+y}{2})}$.

Keywords

References

  1. J. Baker, The stability of the cosine equations, Proc. Amer. Math. Soc. 80 (1980), 411-416. https://doi.org/10.1090/S0002-9939-1980-0580995-3
  2. J. Baker, J. Lawrence and F. Zorzitto, The stability of the equation f(x + y) = f(x) + f(y), Proc. Amer. Math. Soc. 74 (1979), 242-246.
  3. G. L. Forti, Hyers-Ulam stability of functional equations in several variables, Aequationes Math. 50 (1995), 146-190.
  4. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approxi- mately 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. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  6. D.H. Hyers, G. Isac, and Th.M. Rassias, Stability of functional equations in several variables, Birkhauser-Basel-Berlin(1998).
  7. K.W. Jun, G.H. Kim and Y.W. Lee, Stability of generalized gamma and beta functional equations, Aequation Math. 60(2000), 15-24. https://doi.org/10.1007/s000100050132
  8. S.-M. Jung, On the general Hyers-Ulam stability of gamma functional equation, Bull. Korean Math. Soc. 34 No 3 (1997), 437-446.
  9. S.-M. Jung, On the stability of the gamma functional equation, Results Math. 33 (1998), 306-309. https://doi.org/10.1007/BF03322090
  10. G.H. Kim, and Y.W. Lee, The stability of the beta functional equation, Babes- Bolyai Mathematica, XLV (1) (2000), 89-96.
  11. Y.W. Lee, On the stability of a quadratic Jensen type functional equation, J. Math. Anal. Appl. 270 (2002) 590-601. https://doi.org/10.1016/S0022-247X(02)00093-8
  12. Y.W. Lee and G.H. Kim, Stability of the reciprocal di erence and adjoint func- tional equations in m-variables, J. of the Chungcheong Math. Soc. 23 (2010), 731-739.
  13. 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
  14. K. Ravi, J. M. Rassias and B. V. Senthil Kumar, lam stability of reciprocal di erence and adjoint functional equqtions , to appear.
  15. S.M. Ulam, Problems in Modern Mathematics, Proc. Chap. VI. Wiley. NewYork, 1964.