On the Functional Equation
In this paper we solve the functional equationH [tau(F,G), chi (F,G)] = H (F,G)where the unknowns tau and chi are two semigroups on a space of distribution functions, and H is a given pointwise binary operation on this space satisfying some regularity conditions.
In this note we solve the inhomogeneous Cauchy functional equation f(x+y) - f(x) - f(y) = d(x,y), x,y belonging to R, in the case where d is bounded.