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Zbl 0939.39016
Another logarithmic functional equation.
(English)
[J] Aequationes Math. 58, No.3, 260-264 (1999). ISSN 0001-9054; ISSN 1420-8903/e

The author shows that for real valued functions $f$ from the set of positive reals $(0, \infty)$ into the set of real numbers $R$, the classical Cauchy equation $f(xy)=f(x) + f(y)$ is equivalent to the condition: $f(x + y) - f(x) - f(y) = f(x^{-1} + y^{-1})$.
[C.Alsina (Barcelona)]
MSC 2000:
*39B22 Functional equations for real functions

Keywords: equivalent functional equation; Cauchy equation; logarithmic functional equation

Cited in: Zbl 1044.39018

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