Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 79893, 13 pages
doi:10.1155/2007/79893
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

Recommended by H. Bevan Thompson

Abstract

In this paper, we reformulate and prove the Hyers-Ulam-Rassias stability theorem of the cubic functional equation f(ax+y)+f(ax−y)=af(x+y)+af(x−y)+2a(a2−1)f(x) for fixed integer a with a≠0,±1 in the spaces of Schwartz tempered distributions and Fourier hyperfunctions.