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On the stability of the general Euler-Lagrange functional equation. (English) Zbl 0884.47040
The author solves a stability problem for the general 2-dimensional Euler-Lagrange functional inequality \[ |f(a_1x_1+a_2x_2)+f(a_1x_1-a_2x_2)-(a_1^2+a_2^2)[f(x_1)+f(x_2)]|\leq c \] for all 2-dimensional vectors \((x_1,x_2)\in X^2\), with normed linear space \(X\), a nonnegative constant \(c\) (independent of \(x_1,x_2\)), mapping \(f:X\to Y\), where \(Y\) is a complete normed linear space, and any fixed reals \(a_1,a_2\) such that \(a_1^2+a_2^2\neq 0\).

47J05 Equations involving nonlinear operators (general)
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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