一类推广的Dhombres方程的实连续解  

Real continuous solutions of a class of generalized Dhombres equations

作　　者：袁甜真 徐冰[1] YUAN Tian-Zhen;XU Bing(School of Mathematics,Sichuan University,Chengdu 610064,China)

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2022年第6期1-6,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11771307)。

摘　　要：本文研究一类推广的Dhombres方程f^(n)(x)=(f(x))^(m)/x^(m-1)的实连续解问题.基于函数方程的迭代理论、多项式型迭代函数方程的特征理论及降次技术,本文给出了该方程的所有实连续解,其中m,n∈N\{0,1},m≠n,f是(0,+∞)上的连续自映射,f^(n)是f的n次迭代.In this paper,we consider real continuous solutions of a class of generalized Dhombres equation f^(n)(x)=(f(x))^(m)/x^(m-1),where m,n∈N\{0,1},m≠n,f maps(0,+∞)into itself continuously and f^(n) is the n-th iterate of f.By using the iterative theory of functional equations,characteristic theory of polynomial-like iterative equations and a technique of reducing order,we give all real continuous solutions of these equations.

关 键 词：Dhombres方程 特征理论 降次 

分 类 号：O171[理学—数学]