一类涉及线性分式变换函数方程的精确解

Exact Solutions of a Class of Functional Equations Involving Linear Fractional Transformation

研究了一类涉及线性分式变换函数方程的精确解.对于其中一类简单的函数方程,给出了所有情形下的幂级数解.阐明了这类函数方程与一类涉及线性分式变换函数方程解之间的关系.通过不同情形下的具体例子,展示了求解函数方程的方法。

Exact solutions are studied for a class of linear functional equations involving linear fractional transformation.Among them,power series solutions are given for a special kind of functional equations in all cases.Using the conjugate,the relation is expounded between this class of functional equations and the functional equations involving linear fractional transformations.By some concrete examples under different situations,the method is presented to solve this kind of functional equations.