바로가기메뉴

본문 바로가기 주메뉴 바로가기

logo

  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

Article Contents

Prev Next
e-Submission

Vol.17 No.4

Citation Share

STABILITY OF FUNCTIONAL EQUATIONS RELATED TO THE EXPONENTIAL AND BETA FUNCTIONS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2010, v.17 no.4, pp.363-372
Lee, Young-Whan
Lee,, Y. (2010). STABILITY OF FUNCTIONAL EQUATIONS RELATED TO THE EXPONENTIAL AND BETA FUNCTIONS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 17(4), 363-372.

Abstract

In this paper we obtain the Hyers-Ulam stability of functional equations <TEX>$f(x+y)=f(x)+f(y)+In\;{\alpha}^{2xy-1}$</TEX> and <TEX>$f(x+y)=f(x)+f(y)+In\;{\beta(x,y)^{-1}$</TEX> which is related to the exponential and beta functions.

keywords
Cauchy functional equation, exponential functional equation, beta functional equation, stability of functional equation, solution of functional equation

Reference

1.

Lee, Y.W.;Choi, B.M.. (2004). The stability of Cauchy's gamma-beta functional equation. Journal of Mathematical Analysis and Applications, 299(2), 305-313. 10.1016/j.jmaa.2003.12.050.

2.

3.

Jun, K.-W.;Lee, Y.-H.. (2004). A generalization of the Hyers-Ulam-Rassias stability of the Pexiderized quadratic equations. Journal of Mathematical Analysis and Applications, 297(1), 70-86. 10.1016/j.jmaa.2004.04.009.

4.

5.

(2007). . J. Chungcheong Math Soc., 20, 503-514.

6.

(2002). . Math. Inequal. Appl., 5, 707-710.

7.

8.

Rassias, Themistocles M.;Semrl, Peter. (1992). On the Behavior of Mappings which do not Satisfy Hyers-Ulam Stability. Proceedings of the American Mathematical Society, 114(4), 989-993. 10.1090/S0002-9939-1992-1059634-1.

9.

Gavruta, P.. (1994). A Generalization of the Hyers-Ulam-Rassias Stability of Approximately Additive Mappings. Journal of Mathematical Analysis and Applications, 184(3), 431-436. 10.1006/jmaa.1994.1211.

10.

Hyers, D H. (1941). On the Stability of the Linear Functional Equation.. Proceedings of the National Academy of Sciences, 27(4), 222-224. 10.1073/pnas.27.4.222.

11.

Lee, Y.W.. (2002). On the stability of a quadratic Jensen type functional equation. Journal of Mathematical Analysis and Applications, 270(2), 590-601. 10.1016/S0022-247X(02)00093-8.

12.

(2000). . Bull. Institute of Math. Academia Sinica, 28, H3-H6.

13.

Lee, Y.W.;Choi, B.M.. (2004). The stability of Cauchy's gamma-beta functional equation. Journal of Mathematical Analysis and Applications, 299(2), 305-313. 10.1016/j.jmaa.2003.12.050.

14.

Gil&aacute;nyi, A.. (2001). Eine zur Parallelogrammgleichung &auml;quivalente Ungleichung. Aequationes Mathematicae, 62(3), 303-309. 10.1007/PL00000156.

15.

16.

Fechner, W&lstrok;odzimierz. (2006). Stability of a functional inequality associated with the Jordan &ndash; von Neumann functional equation. Aequationes mathematicae, 71(1), 149-161. 10.1007/s00010-005-2775-9.

17.

Gajda. (1991). . International Journal of Mathematics and Mathematical Sciences, 14(3), 431-434. 10.1155/S016117129100056X.

18.

R&auml;tz, J&uuml;rg. (2003). On inequalities associated with the Jordan-von Neumann functional equation. Aequationes Mathematicae, 66(1), 191-2000. 10.1007/s00010-003-2684-8.

19.

Rassias, Themistocles M.. (1978). On the Stability of the Linear Mapping in Banach Spaces. Proceedings of the American Mathematical Society, 72(2), 297-300. 10.1090/S0002-9939-1978-0507327-1.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

e-Submission OA Policy