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On the stability of \(n\)-dimensional quadratic functional equation. (English) Zbl 1101.39304
Summary: We investigate a generalization of the stability of a new quadratic functional equation \(f(\sum_{i=1}^n x_i) + \sum_{1 \leq i < j \leq n} f(x_i-x_j) = n \sum_{i=1}^n f(x_i) (n \geq 2)\) in the spirits of Hyers, Ulam, Rassians and Gavruta.

MSC:
39B52 Functional equations for functions with more general domains and/or ranges
39B72 Systems of functional equations and inequalities
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