Related Equations

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 : ℝ^N → 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.