Stability of Cubic Functional Equation in the Spaces of Generalized Functions

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.