On the stability of the quadratic mapping in normed spaces.

*(English)*Zbl 0986.39015The problem of stability of the following functional equation (so-called the quadratic functional equation)
\[
f(x+y)+f(x-y) =2f(x)+2f(y) \tag{1}
\]
as well as some other functional equations is investigated. The author utilized some ideas contained in the papers of Skof, Czerwik and Gavruta. It is worth to emphasize that the results obtained for the equation (1) are just the particular cases of the results proved by the reviewer [in: Stability of Mappings of Hyers-Ulam Type (ed. by Th. M. Rassias and J. Tabor), Hadronic Press, Florida, 81-91 (1994; Zbl 0844.39008)]. The results concerning some other functional equations are interesting. The methods of proofs are close to the well known idea of Hyers sequences, widely used in the theory of stability of functional equations.

Reviewer: Stefan Czerwik (Gliwice)