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Hyperstability of general linear functional equation. (English) Zbl 1341.39013
Let \(X,Y\) be linear spaces over the real or over the complex field, \(g: X\to Y\), \(A,a_{ij}\in\mathbb{R}\) or \(\mathbb{C}\), \(A_i\not=0\). The main theorem is about hyperstability of the following functional equation \[ \sum_{i=1}^mA_ig\left(\sum_{j=1}^na_{ij}x_j\right)+A=0, \] assuming certain side conditions for the control function.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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