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Solution of Hyers-Ulam stability problem for generalized Pappus’ equation. (English) Zbl 1070.39029
The authors generalize the famous Pappus’ identity and introduce a new functional equation \[ n^2 f(x+my) + mnf(x-my) = (m+n)(nf(x) + mf(ny)) \tag \(*\) \] for given positive integers \(m\) and \(n\). By applying the direct method, they prove the Hyers-Ulam-Rassias stability of the equation (\(*\)) for a class of functions \(f : X \to Y\), where \(X\) is a vector space and \(Y\) is a Banach space.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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