FOR THE HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION

  • Published : 2004.05.01

Abstract

In this paper, we obtain the general solution of a quadratic functional equation $b^2f(\frac{x+y+z}{b})+f(x-y)+f(x-z)=\;a^2[f(\frac{x-y-z}{a})+f(\frac{x+y}{a})+f(\frac{x+z}{a})]$ and prove the stability of this equation.

Keywords

References

  1. Functional Equations in Several Variables J. Aczel;J. Dhombres
  2. Aequationes Math. v.27 Remarks on the stability of functional equations P. W. Cholewa
  3. Abh. Math. Sem. Univ. Hamburg v.62 On the stability of the quadratic mapping in normed spaces S. Czerwik
  4. J. Math. Anal. Appl. v.184 A generalization of the Hyers- Ulam-Rassias stability of approzimately additive mapping P. Gkvruta
  5. Publ. Math. Debrecen v.48 The Generalized Hyers- Ulam stability of a class of functional equations A. Grabiec
  6. Proc. Natl. Acad. Sci. v.27 On the stability of the linear functional equation D. H. Hyers
  7. Aequationes Math. v.44 Approzimate homomorphisms D. H. Hyers;Th. M. Rassias
  8. Function inequalites of for approzimately additive mappings Stability of Mapping of Heyers-Ulam Type G. Isac;Th. M. Rassias;Th. M. Rassia(ed.);J. Tabor(ed.)
  9. Math. Inequal. & Appl. v.4 no.1 On the Hyers- Ulam-Rassias stability of a pexiderized quadratic inequality K.-W. Jun;Y.-H. Lee
  10. J. Math. Anal. Appl. v.222 On the Hyers- Ulam stability of the functional equations that have the quadratic property S.-M. Jung
  11. J. Math. Anal. Appl. v.232 On the Hyers-Ulam-Rassias stability of a quadratic functional equation S.-M. Jung
  12. Korean J. Comput. & Appl. Math. v.9 Stability of a quadratic Jensen type functional equations S. H. Lee
  13. Result. Math. v.27 Quadratic functional equation and inner product spaces Pl. Kannappan
  14. Aequationes Math. v.43 On Jensen's functional equation J. C. Parnami;H. L. Vasudeva
  15. Proc. Amer. Math. Soc. v.72 On the stability of the linear mapping in Banach spaces Th. M. Rassias
  16. Rend. Sem. Mat. Fis. Milano v.53 Proprietd locali e approssimazione di operatori F. Skof
  17. J. Math. Anal. Appl. v.250 Hyars- Ulam stability of a Jensen type functional equations T. Trif
  18. Problems in Modern Mathematics S. M. Ulam