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Zbl 1079.39019
A third logarithmic functional equation and Pexider generalizations.
(English)
[J] Aequationes Math. 70, No. 1-2, 117-121 (2005). ISSN 0001-9054; ISSN 1420-8903/e

If $f: ] 0, \infty [ \to R$ is a real valued function defined on the set of positive reals one may consider the three functional equations: (1) $f(x+y) - f(xy) = f(1/x + 1/y)$, (2) $f(x + y) - f(x) - f(y) = f(1/x, + 1/y )$, (3) $f(xy ) = f(x) + f(y)$. The authors show that the three equations are equivalent. They determine also the general solution of the Pexider equation corresponding to (1) and they find the twice differentiable solutions of the Pexider equation corresponding to (2).
[Claudi Alsina (Barcelona)]
MSC 2000:
*39B22 Functional equations for real functions

Keywords: logarithmic functional equation; Pexider equations

Cited in: Zbl 1130.39018

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