Stability of quadratic functional equations in tempered distributions
Department of Mathematics, Sogang University, Seoul, 121-741, Republic of Korea
Journal of Inequalities and Applications 2012, 2012:177 doi:10.1186/1029-242X-2012-177Published: 16 August 2012
We reformulate the following quadratic functional equation:
as the equation for generalized functions. Using the fundamental solution of the heat equation, we solve the general solution of this equation and prove the Hyers-Ulam stability in the spaces of tempered distributions and Fourier hyperfunctions.