Generalized fundamental equation of information of multiplicative type (Q1088080)

Let \(I=]0,1[^ n\) be the n-dimensional open unit interval, and \(D=\{(x,y)| x,y,x+y\in I\}\). The authors determine the general solution of the functional equation \[ f(x)+\mu (1-x)g(y/(1-x))=h(y)+\mu (1-y)k(x/(1-y)),\text{ for all } (x,y)\in D \] where f,g,h,k,\(\mu\) :I\(\to R\) are unknown functions and the function \(\mu\) is multiplicative.