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Solutions and the generalized Hyers-Ulam-Rassias stability of a generalized quadratic-additive functional equation. (English) Zbl 1217.39035

Summary: We study general solutions and generalized Hyers-Ulam-Rassias stability of the following \(n\)-dimensional functional equation \(f(\sum^k_{i=1} x_i) + (k - 2) \sum^k_{i=1} f(x_i) = \sum^k_{i=1} \sum^k_{j=1, j>i} f(x_i + x_j), k \geq 3\), on non-Archimedean normed spaces.

MSC:

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