Monotonic Solutions of a Functional Equation Arising from Simultaneous Utility Representations

The functional equation ?(h(x)) ? ?(h(y)) + ?(y) = ?(h(x ? y) + y) was solved by Aczél, Luce and Marley on the assumption that the functions are different iable. They posed the question of its strictly monotonic continuous solutions. The problem is solved using a uniqueness theorem. The continuity assumption on the functions is removed and the equation is also solved on a restricted domain.