Advances in Difference Equations
Volume 2009 (2009), Article ID 838347, 16 pages
doi:10.1155/2009/838347
Research Article

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

Received 6 August 2008; Revised 15 December 2008; Accepted 14 January 2009

Academic Editor: Rigoberto Medina

Copyright © 2009 Young-Su Lee and Soon-Yeong Chung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.