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On the Ulam stability of an \(n\)-dimensional quadratic functional equation. (English) Zbl 1329.39034
Summary: We construct a new \(n\)-dimensional quadratic functional equation with constant coefficients \[ \sum_{i,j=1}^n f(x_i+x_j) = 2 \sum_{1\leq i < j \leq n} f(x_i-x_j) + 4f \left( \sum_{i=1}^n x_i \right). \] And then, we study the Ulam stability of the preceding equation in a real normed space and a non-Archimedean space, respectively.

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
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