ON THE STABILITY OF FUNCTIONAL EQUATIONS IN n-VARIABLES AND ITS APPLICATIONS

Title & Authors
ON THE STABILITY OF FUNCTIONAL EQUATIONS IN n-VARIABLES AND ITS APPLICATIONS
KIM, GWANG-HUI;

Abstract
In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form \$f(\varphi(X))\;
Keywords
functional equation, gamma;beta and G-function;Hyers-Ulam stability;Hyers-Ulam-Rassias stability;
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.
H. Alzer, Remark on the stability of the Gamma functional equation, Results Math. 35 (1999), 199-200

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

3.
D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc. 57 (1951), 223-237

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, Rocznik 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 the Functional Equations in Several Variables, Birkhauser Verlag, 1998

8.
D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), 125-153

9.
G. Isac and Th. M. Rassias, On the Hyers-Ulam stability of Ã-additive mappings, J. Approx. Theory 72 (1993), 131-137

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

11.
S.-M. Jung, On the general Hyers-Ulam stability of gamma functional equation, Bull. Korean Math. Soc. 34 (1997), 437-446

12.
S.-M. Jung, On the modified Hyers-Ulam-Rassias stability of the functional equation for gamma function, Mathematica 39 (1997), 233-237

13.
S.-M. Jung, On the stability of gamma functional equation, Results Math. 33 (1998), 306-309

14.
G. H. Kim, On the stability of generalized Gamma functional equation, Internat. J. Math. & Math. Sci. 23 (2000), 513-520

15.
G. H. Kim, A generalization of the Hyers-Ulam-Rassias stability of the Beta functional equation, Publ. Math. Debrecen 59 (2001), 111-119

16.
G. H. Kim, A generalization of Hyers-Ulam-Rassias stability of a G-functional equation, Math. Inequal. Appl., to appear

17.
G. H. Kim, Y.W. Lee, The stability of the beta functional equation, Studia Univ. 'Babes-Bolyai', Mathematica 40 (2000), 89-96

18.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300

19.
Th. M. Rassias, On the modified Hyers-Ulam sequence, J. Math. Anal. Appl. 158 (1991), 106-113

20.
Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), 23-130

21.
Th. M. Rassias, On the stability of functional equations in Banach space, J. Math. Anal. Appl. 251 (2000), 264-284

22.
Th. M. Rassias (ed.), Functional Equations and Inequalities, Kluwer Academic Publishers, Dordrecht, 2000

23.
Th. M. Rassias (ed.), Functional Equations, Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 2003

24.
Th. M. Rassias and P. Semrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc. 114 (1992), 989-993

25.
Th. M. Rassias and J. Tabor, Stability of Mappings of Hyers-Ulam Type, Hadronic Press Inc., Florida, 1994

26.
T. Trip, On the stability of a general gamma-type functional equation, Publ. Math. Debrecen 60 (2002), 47-62

27.
S. M. Ulam, Problems in Modern Mathematics, Chap. VI , Science editions, Wiley, New York, 1964