| 摘要: |
| 设r是个给定的正数,用D=Dr表示复平面C内以原点为心r为半径的闭圆盘.令A(D,D)={f:f为从D到D的连续映射,并且f|D0解析}.设G:Dn+1 →C连续(n ≥2),并且G|(Dn+1)0解析,g1,…,gn ∈A(D,D),本文讨论了迭代函数方程G(z,f(g1(z)),…,fn(gn(z)))=0,给出该方程在A(D,D)中有解和有唯一解的条件. |
| 关键词: 迭代函数方程 解析解 差商 函数空间 紧致凸集 |
| DOI： |
| 投稿时间：1999-07-09 |
| 基金项目:国家自然科学基金资助项目。 |
|
| Analytic Solutions of a Class of Iterative Functional Equations |
|
Liu Xinhe
|
| (Dept. of Math. & Info., Guangxi Univ., 10 Xixiangtanglu, Nanning, Guangxi, 530004, China) |
| Abstract: |
| Let r be a given positive number.Denote by D=Dr the closed disc in the complex plane C whose center is the origin and radius is r.Write A(D,D)={f:f is a continuous map from D to itself,and f|D0 is analytic}.Suppose G:Dn+1 →C is a continuous map (n ≥ 2),and G|(Dn+1) 0 is analytic.Let g1,…,gn∈A(D,D) be given maps.In this paper, we study the iterative functional equation G(z,f(g1(z)),…,fn(gn(z)))=0 and give some conditions for the equation to have a solution and a unique solution in A(D,D). |
| Key words: iterative functional equation analytic solution difference quotient functional space compact convex set |
