Stability of Cubic Functional Equation in the Spaces of Generalized Functions

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.