On the general solution of a system of functional equations (Q1065296)

The author determines the general solution of the functional equations system (1) g(x,z)-\(g(x+y,z)=g(x,y)-g(x+z,y),\) \((2)g(x,y)+g(x,z)-g(x,y+z)=g(y,x)+g(y,z)-g(y,x+z),\) for all real x, y, z, which has a connection with theoretical physics. As he mentions, the solutions of (1) have been found by \textit{C. T. Ng} [Inf. Control 41, 214-231 (1979; Zbl 0423.94006)] and by the reviewer [Can. Math. Bull. 22, 433-448 (1979; Zbl 0434.94002)]. These solutions can be put into (2) to get the author's result. He provides a more direct proof in this special case.