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The hyperstability of general linear equation via that of Cauchy equation. (English) Zbl 1417.39085
The task of a hyperstability problem is to understand when a function which approximately satisfies a functional equation is also a solution of it. M. Piszczek [Aequationes Math. 88, No. 1–2, 163–168 (2014; Zbl 1304.39033)] proved a hyperstability result for general linear equation $$f(ax + by) = Af(x) + Bf(y)$$. J. Brzdęk [Acta Math. Hung. 141, No. 1–2, 58–67 (2013; Zbl 1313.39037)] and proved the hyperstability of the Cauchy equation $$f(x+y)=f(x)+f(y)$$. In the paper under review, the authors show that the result of Piszczek can be deduced from that of Brzdęk.

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B62 Functional inequalities, including subadditivity, convexity, etc. 47H14 Perturbations of nonlinear operators 47J20 Variational and other types of inequalities involving nonlinear operators (general)
##### Keywords:
hyperstability; general linear equation; Cauchy equation
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##### References:
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