ON THE STABILITY OF THE GENERALIZED G-TYPE FUNCTIONAL EQUATIONS

Title & Authors
ON THE STABILITY OF THE GENERALIZED G-TYPE FUNCTIONAL EQUATIONS
KIM, GWANG-HUI;

Abstract
In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $\small{f({{\varphi}(x)) = {\Gamma}(x)f(x)}$. As a consequence in the cases $\small{{\varphi}(x) := x+p:= x+1}$, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.
Keywords
Functional equation;Hyers-Ulam stability;Hyers-Ulam­Rassias stability;G-function;double gamma function;
Language
English
Cited by
1.
ON FUNCTIONAL INEQUALITIES ASSOCIATED WITH JORDAN-VON NEUMANN TYPE FUNCTIONAL EQUATIONS,;

대한수학회논문집, 2008. vol.23. 3, pp.371-376
References
1.
E. W. Barnes, The theory of the double gamma function, Proc. Roy. Soc. London Ser. A 196 (1901), 265-388

2.
E. W. Barnes, The theory of the G-function, Quart. J. Math. 31 (1899), 264-314

3.
J. Choi and H. M. Srivastava, Certain classes of series involving the Zeta func- tion, J. Math. Anal. Appl. 231 (1999), 91-117

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.
R. Ger, Superstability is not natural, Roczik Nauk.-Dydakt. Prace Mat. 159 (1993), 109-123

6.
D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222-224

7.
D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of functional equation in Several Variables, Birkhauser, Basel, 1998

8.
S. M. Jung, On the modified Hyers-Ulam-Rassias stability of the functional equation for gamma function, Mathematica 39(62) (1997), no. 2, 233-237

9.
S. M. Jung, On the stability of G-functional equation, Results Math. 33 (1998), 306-309

10.
K. W. Jun, G. H. Kim and Y. W. Lee, Stability of generalized gamma and beta functional equations, Aequationes Math. 60 (2000), 15-24

11.
G. H. Kim, On the stability of generalized Gamma functional equation, Internat. J. Math. Math. Sci. 23 (2000), 513-520

12.
G. H. Kim, Stability of the G-functional equation, J. Appl. Math. Comput. 23 (2000), 513-520

13.
G. H. Kim, The stability of generalized Gamma functional equation, Nonlinear Studies. 7(1) (2000), 92-96

14.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300

15.
S. M. Ulam, 'Problems in Modern Mathematics' Chap. VI, Science edit. Wiley, New York, 1960