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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 $$a_1^2+a_2^2\neq 0$$.

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