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Hyers-Ulam stability for a class of quadratic functional equations via a typical form. (English) Zbl 1291.39053

Summary: We investigate the following typical form of a certain class of quadratic functional equations: \(f(ax+by)+f(ax-by)+c[f(x+y)+f(x-y)-2f(x)-2f(y)]=2a^2f(x)+2b^2f(y)\). Furthermore, we provide a systematic program to prove the generalized Hyers-Ulam stability for the class of functional equations via the stability for the typical form.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
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