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 ---> 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 equation f(ux + (L − 1)vy, xv + yu + (L − 2)yv, zw + (μ −1)ts, zs+tw+(μ−2)ts) = g(x, y, z, t) h(u, v,w, s), where f, g, h : K4 ---> K are unknown functions. We do not require any continuity condition on the unknown functions. This paper may be considered as a continuation to the paper [2].