Stability of Quartic Functional Equations in the Spaces of Generalized Functions

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 . In 1978, Rassias 3 generalized Hyers’ result to the unbounded Cauchy difference. During the last decades, stability problems of various functional equations have been extensively studied and generalized by a number of authors see 4–9 . The terminology Hyers-UlamRassias stability originates from these historical backgrounds and this terminology is also applied to the cases of other functional equations. For instance, Rassias 10 investigated stability properties of the following functional equation