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

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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Correspondence to Young-Su Lee.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Lee, YS. Stability of a Quadratic Functional Equation in the Spaces of Generalized Functions. J Inequal Appl 2008, 210615 (2008). https://doi.org/10.1155/2008/210615

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

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