The following functional equations are also referred to as Cauchy’s equations (Cauchy ; cf. also Aczél )
$$ f(x + y) = f(x)f(y), $$
$$ f(xy) = f(x) + f(y), $$
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.
$$ f(xy) = f(x)f(y), $$
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