Browse > Article
http://dx.doi.org/10.4134/CKMS.2005.20.1.093

ON THE STABILITY OF THE GENERALIZED G-TYPE FUNCTIONAL EQUATIONS  

KIM, GWANG-HUI (Department of Mathematics Kangnam University)
Publication Information
Communications of the Korean Mathematical Society / v.20, no.1, 2005 , pp. 93-106 More about this Journal
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 $f({{\varphi}(x)) = {\Gamma}(x)f(x)$. As a consequence in the cases ${\varphi}(x) := x+p:= x+1$, 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;
Citations & Related Records
연도 인용수 순위
  • Reference
1 E. W. Barnes, The theory of the double gamma function, Proc. Roy. Soc. London Ser. A 196 (1901), 265-388
2 P. Gavruta, A Generalization of the Hyers-Ulam-Rassias stability of approxi- mately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436   DOI   ScienceOn
3 R. Ger, Superstability is not natural, Roczik Nauk.-Dydakt. Prace Mat. 159 (1993), 109-123
4 D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222-224   DOI   ScienceOn
5 D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of functional equation in Several Variables, Birkhauser, Basel, 1998
6 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
7 S. M. Jung, On the stability of G-functional equation, Results Math. 33 (1998), 306-309   DOI   ScienceOn
8 K. W. Jun, G. H. Kim and Y. W. Lee, Stability of generalized gamma and beta functional equations, Aequationes Math. 60 (2000), 15-24   DOI   ScienceOn
9 G. H. Kim, On the stability of generalized Gamma functional equation, Internat. J. Math. Math. Sci. 23 (2000), 513-520   DOI
10 G. H. Kim, Stability of the G-functional equation, J. Appl. Math. Comput. 23 (2000), 513-520
11 G. H. Kim, The stability of generalized Gamma functional equation, Nonlinear Studies. 7(1) (2000), 92-96
12 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300
13 S. M. Ulam, 'Problems in Modern Mathematics' Chap. VI, Science edit. Wiley, New York, 1960
14 J. Choi and H. M. Srivastava, Certain classes of series involving the Zeta func- tion, J. Math. Anal. Appl. 231 (1999), 91-117   DOI   ScienceOn
15 E. W. Barnes, The theory of the G-function, Quart. J. Math. 31 (1899), 264-314