Stability of a Quadratic Functional Equation in the Spaces of Generalized Functions
© Young-Su Lee. 2008
Received: 30 June 2008
Accepted: 20 August 2008
Published: 8 September 2008
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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