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The Ulam stability problem in approximation of approximately quadratic mappings by quadratic mappings. (English) Zbl 1055.39041
The author proves by very standard methods the stability in the sense of Ulam of the functional equation \[ Q(a_1x_1+a_2x_2)+Q(a_2x_1-a_1x_2)=(a_1^2+a_2^2)[Q(x_1)+Q(x_2)] \] where \(Q:X \to Y\), \(X, Y\) are normed linear space and \(Y\) is complete, and \((a_1,a_2) \in \mathbb R^2 \setminus (0,0)\) is arbitrarily fixed.

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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