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On the generalized Hyers-Ulam-Rassias stability of a quadratic functional equation. (English) Zbl 0983.39014
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 the functional equations in mathematical analysis, Hadronic Press, Palm Harbor (2001; Zbl 0980.39024)] of functional equation \(f(x+y+z) + f(x-y) + f(y-z) + f(z-x) = 3 f(x) + 3 f(y) + 3 f(z)\) in the spirit of Hyers, Ulam, Rassias and Găvruţă. In this paper, the authors also treat the Hyers-Ulam stability of the above equation on a restricted domain.

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