ON THE STABILITY OF N-DIMENSIONAL QUADRATIC FUNCTIONAL EQUATION

  • Bae, Jae-Hyeong (Department of Mathematics, Chungnam National University)
  • Published : 2001.01.01

Abstract

In this paper, we investigate a generalization of the stability of a new quadratic functional equation f(∑(sub)i=1(sup)n x(sub)i)+∑(sub)1$\leq$i$\leq$n f(x(sub)i-x(sub)j) = n∑(sub)i=1(sup)n f(x(sub)i) (n$\geq$2) in the spirits of Hyers, Ulam, Rassias and Gavruta.

Keywords

References

  1. Bull. Korean. Math. Soc. v.37 On the stability of 3-dimensional quadratic functional equation J. H. Bae
  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 normal spaces S. Czerwik
  4. J. Math. Anal. and Appl. v.184 A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings P. Gavruta
  5. Proc. Nat. Acad. Sci. U. S. A. v.27 On the stability of the linear functional equation D. H. Hyers
  6. J. Math. Anal. Appl. v.239 On Hyers-Ulam-Rassias stability of the pexider equation K. W. Jun;D. S. Shin;B. D. Kim
  7. J. Math. Anal. Appl. v.222 On the Hyers-Ulam stability of the functional equations that have the quadratic property S. -M. Jung
  8. Results Math. v.27 Quadratic functional equation and inner product spaces PI. Kannappan
  9. Chinese J. Math. v.20 On the stability of the Euler-Lagrange functional equation Th. M. Rassias
  10. Proc. Amer. Math. Soc. v.72 On the stability of the linear mapping in Banach spaces Th. M. Rassias
  11. Rend. Sem. Mat. Fis. Milano v.53 Proprieta localie approssimazione di operatori F. Skof
  12. Chap. Ⅵ Problems in Modern Mathematics S. M. Ulam