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On the generalized Hyers-Ulam-Rassias stability of an \(n\)-dimensional quadratic function equation. (English) Zbl 0983.39013
The authors examine the Hyers-Ulam-Rassias stability [see D. H. Hyers, G. Isac and Th. M. Rassias, Stability of functional equations in several variables, Birkhäuser, Boston (1998; Zbl 0907.39025) and Soon-Mo Jung, Hyers-Ulam-Rassias stability of functional equations in mathematical analysis, Hadronic Press, Palm Harbor (2001; Zbl 0980.39024)] of the following functional equation \[ f\left (\sum_{i=1}^n x_i \right) + \sum_{1\leq i\leq j \leq n} f(x_i - x_j) = n \sum_{i=1}^n f(x_i) \quad (n \geq 2) \] in the spirit of Hyers, Ulam, Rassias and Găvruţă.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
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