Advances in Difference Equations
Volume 2009 (2009), Article ID 838347, 16 pages
doi:10.1155/2009/838347
Stability of quartic functional equations in the spaces of generalized functions
Young-Su Lee1
and Soon-Yeong Chung2
1Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea
2Department of Mathematics and Program of Integrated Biotechnology, Sogang University, Seoul 121-741, South Korea
Abstract
We consider the general solution of quartic functional equations and prove the Hyers-Ulam-Rassias stability. Moreover, using the pullbacks and the heat kernels we reformulate and prove the stability results of quartic functional equations in the spaces of tempered distributions and Fourier hyperfunctions.