Open Access

Stability of a Quadratic Functional Equation in the Spaces of Generalized Functions

Journal of Inequalities and Applications20082008:210615

https://doi.org/10.1155/2008/210615

Received: 30 June 2008

Accepted: 20 August 2008

Published: 8 September 2008

Abstract

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.

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Authors’ Affiliations

(1)
Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology

Copyright

© Young-Su Lee. 2008

This article is published under license to BioMed Central Ltd. 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.