Abstract

In 1839, De Morgan gave a mathematical justification of Gompertz's law of mortality through a composite functional equation, f(x + y) + f(x + z) = f(x + h(y, z)). A slightly more general version of this equation was studied in 1905 by M. Chini. Both solved their equations in the class of differentiable 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 functions.

Author Keywords: law of mortality; composite functional equation; locally bounded solutions