General solutions of some functional equations

In this paper, we determine the general solutions of the functional equation f(ux + (L − 1)vy, xv + yu + (L − 2)yv) = g(x, y) h(u, v), where f, g, h : K2 --- and gt; K are unknown functions and L in K* := K \ {0}, where K = R (resp. C) the real (resp. complexe) field. We also treat the functional eq...