Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 79893, 13 pages
Research Article

Stability of Cubic Functional Equation in the Spaces of Generalized Functions

Young-Su Lee1 and Soon-Yeong Chung2

1Department of Mathematics, Sogang University, Seoul 121-741, South Korea
2Department of Mathematics and Program of Integrated Biotechnology, Sogang University, Seoul 121-741, South Korea

Received 24 April 2007; Accepted 13 September 2007

Academic Editor: H. Bevan Thompson

Copyright © 2007 Young-Su Lee and Soon-Yeong Chung. 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.


In this paper, we reformulate and prove the Hyers-Ulam-Rassias stability theorem of the cubic functional equation f(ax+y)+f(axy)=af(x+y)+af(xy)+2a(a21)f(x) for fixed integer a with a0,±1 in the spaces of Schwartz tempered distributions and Fourier hyperfunctions.