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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.

MSC:

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

Citations:

Zbl 0844.39008
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