DOI QR코드

DOI QR Code

STABILITY OF GENERALIZED EULER-LAGRANGE FUNCTIONAL EQUATIONS

  • Lee, Eun-Hwi (Department of Computer and Information Mathematics Jeonju University) ;
  • Song, Young-Seoung (Department of Computer and Information Mathematics Jeonju University)
  • Received : 2007.01.26
  • Published : 2007.03.25

Abstract

Th. M. Rassias obtained the Hyers-Ulam stability of the general Euler-Lagrange functional equation. In this paper we prove the stability of generlized Euler-Lagrange functional equations in the spirit of Hyers, Ulam, Rassias and G$\breve{a}$vruta.

Keywords

References

  1. G. L. Forti, Hyers-Ulam stability of a functional equations in several variables, Aequationes Math., 50 (1995), 143-190. https://doi.org/10.1007/BF01831117
  2. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436. https://doi.org/10.1006/jmaa.1994.1211
  3. D. H. Hyers, On the stability of the linear functional equation., Proc. Natl. Acad. Sci. U. S. A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  4. D. H. Hyers, G. Isac, and Th. M. Rassias,"Stability of a Functional equations in several variables", Birkhauser, Boston/Basel/Berlin (1998).
  5. D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), 125-153. https://doi.org/10.1007/BF01830975
  6. K. W. Jun, G. H. Kim and Y. W. Lee, Stability of generalized gamma and beta func­tional equations, Aequationes Math. 60 (2000), 15-24. https://doi.org/10.1007/s000100050132
  7. S. M. Jung, Hyers-Ulam-Rassias stability of Jensen's equation and its application, Proc. Amer. Math. Soc. 126 (1998), 3137-3143. https://doi.org/10.1090/S0002-9939-98-04680-2
  8. Y. H. Lee and K. W. Jun, A generalization of the Hyers-Ulam-Rassias stability of Jensen's Equation, J. Math. Anal. Appl., 238 (1999), 305-315. https://doi.org/10.1006/jmaa.1999.6546
  9. Y. W. Lee, The stability of derivatins on Banach algebras, Bull. Institute of Math. Academia Sinica. 28 (2000), 113-116.
  10. Y. W. Lee, A generalized stability of the general Euler-Lagrange functional equation, Comm. Korean Math. Soc. 16 (2001), 607-619.
  11. 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
  12. J. M. Rassias, On the stability of the general Euler-Lagrange functional equation, Demonstratio Math. XXIX (1996), 755-766.
  13. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978page 297-300).
  14. S. M. Ulam, "Problems in Modern Mathematics" Chap. VI, Science editions,Wiley, New York, (1964).