Abstract. In this paper, we determine the general solution of the functional equation f (ux+vy, uy+vx) = g(x, y) h(u, v) where f,g,h: M 2 -» R are unknown functions. We also treat the equation f (ux + vy, uy + vx, zw) = g(x,y,z) h(u,v,w) where /, g,h : R 3 -» R are unknown functions. Our method is elementary and we do not use any regularity conditions. 1991 Mathematics Subject Classification: Primary 39B22.
Introduction Let us define
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