On the generalized Hyers-Ulam stability of a quadratic mapping. (English) Zbl 0995.39008

The Hyers-Ulam stability of some functional equation is investigated. But, in fact, the equation considered by the authors is equivalent to the following quadratic functional equation \[ f(x+y)+f(x-y)=2f(x)+ 2f(y). \] Therefore, all the results contained in the paper as well as the basic ideas can be derived from the work of S. Czerwik [The stability of the quadratic functional equation, in: Stability of mappings of Hyers-Ulam type, (ed. Th. M. Rassias and J. Tabor), Hadronic Press, Palm Harbor, Florida, 81-91 (1994; Zbl 0844.39008)].
Some estimations presented in the paper may be interesting for the reader.


39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges


Zbl 0844.39008