On a Class of Functional Equations in Distribution

In this article, we present the most general solution of the functional equations f xy.qf 1yx. 1yy..sf x 1yy..qf y 1yx.. and f xy.qf x 1yy..q f y 1yx..qf 1yx. 1yy..sf x.qf 1yx.qf y.qf 1yy. in the domain of distributions; and show that for regular distributions the solutions are the same as the classical solutions. These functional equations arise in connection with the characterization of sum form information measures