Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 210615, 12 pages
doi:10.1155/2008/210615
Abstract
Making use of the pullbacks, we reformulate the following
quadratic functional equation: f(x+y+z)+f(x)+f(y)+f(z)=f(x+y)+f(y+z)+f(z+x)
in the spaces of
generalized functions. Also, using the fundamental solution
of the heat equation, we obtain the general solution and
prove the Hyers-Ulam stability of this equation in the spaces
of generalized functions such as tempered distributions and Fourier hyperfunctions.