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The stability of a functional equation of multiplicative derivation type. (English) Zbl 1153.39032
The authors study the stability in the sense of R. Ger of the functional equation \[ f(xy) = M(x)f(y) + M(y)f(x) \quad (x, y \in (0,\infty)) \] of multiplicative derivation type, where \(M: (0,\infty) \to (0,\infty)\) is a multiplicative function. This functional equation was introduced by G. Maksa and Z. Páles [Acta Math. Acad. Paedagog. Nyházi. (N.S.) 17, 107–112 (2001; Zbl 1004.39022)].
MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B22 Functional equations for real functions
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