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.
Highlights
One of the interesting questions concerning the stability problems of functional equations is as follows: when is it true that a mapping satisfying a functional equation approximately must be close to the solution of the given functional equation? Such an idea was suggested in 1940 by Ulam 1
The case of approximately additive mappings was solved by Hyers 2
The terminology Hyers-UlamRassias stability originates from these historical backgrounds and this terminology is applied to the cases of other functional equations
Summary
We consider the general solution of quartic functional equations and prove the Hyers-UlamRassias stability. 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.
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