Research Article
Stability of a Quadratic Functional Equation in the Spaces of Generalized Functions
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, South Korea
Journal of Inequalities and Applications 2008, 2008:210615 doi:10.1155/2008/210615
Published: 8 September 2008Abstract
Making use of the pullbacks, we reformulate the following quadratic functional equation:
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.
