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Stability of Cubic Functional Equation in the Spaces of Generalized Functions

DOI: 10.1155/2007/79893

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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.

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