对d’Alembert型函数方程组的研究

Solution to a System of d'Alembert Functional Equations

将d’Alembert型函数方程f(xy) +f(xy- 1) =f(x) g(y) +h(y)在满足条件 f(xyz) =f(xzy)下的一般解推广到在群上d’Alembert型函数方程组的情形 ,证明了求解定理并确定出一般解 .主要方法是引入新函数 ,把函数方程组分解成独立的已解决的上述方程的形式进行求解 ,同时还使用新的符号 。

In the present study, the solution to the d'Alembert type functional equation f(xy)+f(xy -1 )=f(x)g(y)+h(y) is extended to the study of a system of d'Alembert functional equtions on a group under the condition that the former satisfies f(xyz)=f(xzy) .For this purpose, a new function is introduced and the system of functional equations on a group is decomposed into independent equations. A new symbol is used to show the general solution to a system of functional equations on a group.