摘要
主要提出了如下函数方程问题 :设m ,n是正整数 ,试求出所有的函数f:R→R ,使得对于任何的x ,y∈R ,都有f(xm+y +f(n) (y) ) =2y+(f(x) ) m.本文采用“算两次”方法对第 40届IMO的第 6题 (确定所有的函数f:R→R ,其中R是实数集 ,使得对任意x,y∈R ,恒有f(x -f(y) ) =f(f(y) ) +xf(y) +f(x) - 1成立 )给出一个新的解法 ,对本文所提问题的一种特殊情形“m =2且n =1”给出了完整的解答 .另外 ,还提出了一些相关的函数方程问题 .
In this paper,the author proposed the problem as follows:let m and n be two positive integers, find all functions f:R→R such that f(x m+y+f (n)(y))=2y+(f(x)) m for all x and y in R,here f (n)(y) denote the n_th iteration of f(y).The case 'm=2 and n=1' was solved in this paper,some open problems were proposed in this paper. And the problem 40-IMO-6 (Determine all functions f:RR,here R is the set of all real numbers,such that f(x-f(y))=f(f(y))+x·f(y)+f(x)-1 for all x,y in R) was solved in this paper.
出处
《广州大学学报（自然科学版）》
CAS
2002年第4期8-12,共5页
Journal of Guangzhou University:Natural Science Edition
基金
广州市教委 2 0 0 0年科研项目
