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On the stability of additivity. (English) Zbl 1197.39016
R. Ger and J. Sikorska [Bull. Pol. Acad. Sci., Math. 43, No. 2, 143–151 (1995; Zbl 0833.39007)] proved the stability of the following conditional functional inequality
$x\bot y\quad\text{implies}\quad \|f(x+y)-f(x)-f(y)\|\leq\varepsilon,$
where $$\bot$$ is a given orthogonality relation and $$\varepsilon$$ is a given nonnegative number. In this paper, the authors investigate the stability of the above inequality in a general framework with a new method.

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B55 Orthogonal additivity and other conditional functional equations 39B62 Functional inequalities, including subadditivity, convexity, etc.
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