Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 210615, 12 pages
Research Article

Stability of a Quadratic Functional Equation in the Spaces of Generalized Functions

Young-Su Lee

Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, South Korea

Received 30 June 2008; Accepted 20 August 2008

Academic Editor: László Losonczi

Copyright © 2008 Young-Su Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Making use of the pullbacks, we reformulate the following quadratic functional equation: f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(z+x) in the spaces of generalized functions. Also, using the fundamental solution of the heat equation, we obtain the general solution and prove the Hyers-Ulam stability of this equation in the spaces of generalized functions such as tempered distributions and Fourier hyperfunctions.