Skip to main content
  • Research Article
  • Open access
  • Published:

A Multidimensional Functional Equation Having Quadratic Forms as Solutions

Abstract

We obtain the general solution and the stability of the-variable quadratic functional equation The quadratic form is a solution of the given functional equation.

[123456]

References

  1. Aczél J, Dhombres J: Functional Equations in Several Variables, Encyclopedia of Mathematics and Its Applications. Volume 31. Cambridge University Press, Cambridge, UK; 1989:xiv+462.

    Book  Google Scholar 

  2. Bae J-H, Jun K-W: On the generalized Hyers-Ulam-Rassias stability of an-dimensional quadratic functional equation. Journal of Mathematical Analysis and Applications 2001,258(1):183–193. 10.1006/jmaa.2000.7372

    Article  MathSciNet  MATH  Google Scholar 

  3. Bae J-H, Park W-G: On the generalized Hyers-Ulam-Rassias stability in Banach modules over a -algebra. Journal of Mathematical Analysis and Applications 2004,294(1):196–205. 10.1016/j.jmaa.2004.02.009

    Article  MathSciNet  MATH  Google Scholar 

  4. Bae J-H, Park W-G: On stability of a functional equation with-variables. Nonlinear Analysis: Theory, Methods & Applications 2006,64(4):856–868. 10.1016/j.na.2005.06.028

    Article  MathSciNet  MATH  Google Scholar 

  5. Jung S-M: On the Hyers-Ulam stability of the functional equations that have the quadratic property. Journal of Mathematical Analysis and Applications 1998,222(1):126–137. 10.1006/jmaa.1998.5916

    Article  MathSciNet  MATH  Google Scholar 

  6. Park W-G, Bae J-H: On a bi-quadratic functional equation and its stability. Nonlinear Analysis: Theory, Methods & Applications 2005,62(4):643–654. 10.1016/j.na.2005.03.075

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Won-Gil Park.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Park, WG., Bae, JH. A Multidimensional Functional Equation Having Quadratic Forms as Solutions. J Inequal Appl 2007, 024716 (2007). https://doi.org/10.1155/2007/24716

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/2007/24716

Keywords