On a functional equation in actuarial mathematics

In 1839, De Morgan gave a mathematical justification of Gompertz's law of m ortality through a composite functional equation, f(x + y) f f(x + z) = f(x + h(y, z)). A slightly more general version of this equation was studied i n 1905 by M. Chini. Both solved their equations in the class of differentia ble functions on the real line. Here we solve the equation f(x) + f(x + y) = cf(x + g(y)), which is a generalization of Chini's equation, on intervals in the class of locally bounded functions and in the class of continuous f unctions. (C) 2001 Academic Press.