STABILITY OF MULTIPLICATIVE INVERSE FUNCTIONAL EQUATIONS IN THREE VARIABLES

• Journal title : Honam Mathematical Journal
• Volume 34, Issue 1,  2012, pp.45-54
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2012.34.1.45
Title & Authors
STABILITY OF MULTIPLICATIVE INVERSE FUNCTIONAL EQUATIONS IN THREE VARIABLES
Lee, Eun-Hwi;

Abstract
In this paper, we prove stabilities of multiplicative functional equations in three variables such as $\small{r(\frac{x+y+z}{3})-r(x+y+z)}$=$\small{\frac{2r(\frac{x+y}{2})r(\frac{y+z}{2})r(\frac{z+x}{2})}{r(\frac{x+y}{2})r(\frac{y+z}{2})+r(\frac{y+z}{2})r(\frac{z+x}{2})+r(\frac{z+x}{2})r(\frac{x+y}{2})}}$ and $\small{r(\frac{x+y+z}{3})+r(x+y+z)}$=$\small{\frac{4r(\frac{x+y}{2})r(\frac{y+z}{2})r(\frac{z+x}{2})}{r(\frac{x+y}{2})r(\frac{y+z}{2})+r(\frac{y+z}{2})r(\frac{z+x}{2})+r(\frac{z+x}{2})r(\frac{x+y}{2})}}$.
Keywords
Functional Equation;Stability;
Language
English
Cited by
References
1.
J. Baker, The stability of the cosine equations, Proc. Amer. Math. Soc. 80 (1980), 411-416.

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.

5.
D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224.

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.

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.

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.

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.

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.