STABILITY OF FUNCTIONAL EQUATIONS RELATED TO THE EXPONENTIAL AND BETA FUNCTIONS

  • Lee, Young-Whan (Department of Computer Hacking and Information Security, Daejeon University)
  • 투고 : 2010.08.10
  • 심사 : 2010.11.22
  • 발행 : 2010.11.30

초록

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

키워드

참고문헌

  1. P. Czerwik: Functional Equations and Inequalities in Several Variables. World Scientific Publishing Company, New Jersey, Hong Kong, Singapore and London, 2002.
  2. W. Fechner: Stability of a functional inequalities associated with the Jordan-von Neumann functional equation. Aequations Math. 71 (2006), 149-161. https://doi.org/10.1007/s00010-005-2775-9
  3. Z. Gajda: On stability of additive mappings. Internat. J. Math. Math. Sci. 14 (1991), 431-434. https://doi.org/10.1155/S016117129100056X
  4. P. Gavruta: On the stability of the linear functional equation. Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  5. A. Gilanyi: Eine zur Parallelogrammgleichung quivalente Ungleichung . Aequationes Math. 62 (2001), 303-309. https://doi.org/10.1007/PL00000156
  6. A. Gilanyi: On a problem by K. Nikodem. Math. Inequal. Appl. 5 (2002), 707-710.
  7. A. Gilanyi: A generalization of the Hyers-Ulam- Rassias Stability of approxi-mately additive mappings. J. Math. Anal. Appl. 184 (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211
  8. D.H. Hyers, G. Isac & Th.M. Rassias: Stability of functional equations in several variables. Birkhauser-Basel-Berlin (1998).
  9. K. Jun & Y. Lee: A generalization of the Hyers-Ulam-Rassias stability of the Pexiderized quadratic equations. J. Math. Anal. Appl. 297 (2004), 70-86. https://doi.org/10.1016/j.jmaa.2004.04.009
  10. S.-M. Jung: Hyers-Ulam-Rassias stability of Functional Equations in Mathemat-ical analysis. Hadronic Press Inc., Palm Harbor, Florida (2001).
  11. H. Kim & J. OH: Heyers-Ulam stability of Functional inequalities associated with Cauchy mapping. J. Chungcheong Math Soc. 20 (2007), 503-514.
  12. Y.W. Lee: On the stability of a quadratic Jensen type functional equation. J. Math. Anal. Appl. 270 (2002), 590-601. https://doi.org/10.1016/S0022-247X(02)00093-8
  13. Y.W. Lee: The stability of derivations on Banach algebras. Bull. Institute of Math. Academia Sinica 28 (2000), H3-H6.
  14. Y.W. Lee & B.M. Choi: The stability of Cauchy's gamma-beta functional equation. J. Math. Anal. Appl. 299 (2004), 305-313. https://doi.org/10.1016/j.jmaa.2003.12.050
  15. Y.W. Lee & B.M. Choi: The stability of Cauchy's gamma-beta functional equation. J. Math. Anal. Appl. 299 (2004), 305-313. https://doi.org/10.1016/j.jmaa.2003.12.050
  16. Th.M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72 (1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  17. Th.M. Rassias & P. Semrl: On the behaviour of mappings which do not satisfy Hyers-Ulam stability. Proc. Amer. Math. Soc. 114 (1992), 989-993. https://doi.org/10.1090/S0002-9939-1992-1059634-1
  18. J. Ratz: On inequlities associated with the Jordan-von Neumann functional equation. Aequationes Math. 66 (2003), 191-2000. https://doi.org/10.1007/s00010-003-2684-8
  19. S.M. Ulam: A Collection of the Mathematical Problems. Interscience Pub. New York, 1960.