Abstract

The following functional equations are also referred to as Cauchy’s equations (Cauchy [41]; cf. also Aczél [5])
$$ f(x + y) = f(x)f(y), $$
(13.1.1)
$$ f(xy) = f(x) + f(y), $$
(13.1.2)
$$ f(xy) = f(x)f(y), $$
(13.1.3)
Equation (13.1.1) will be considered for functions f : ℝN → ℝ, whereas equations (13.1.2) and (13.1.3) will be considered only for functions of a real variable, because of the operation of multiplication occurring in the argument.

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Copyright information

© Birkhäuser Verlag AG 2009

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