关于函数方程的若干进展

Some Advances on Functional Eqnations

本文介绍了单实变量的函数方程的若干新进展，包括迭代根、Ｓｃｈｒｏｄｅｒ方程和多项式型迭代方程的结果。基本内容有：Ⅰ．引言：迭代与相关问题；Ⅱ。迭代根：存在性；Ⅲ唯一性、可微性和分枝；Ⅳ．多项式型迭代根方程。

In this paper some new advances on functional equations in a single real variable are introduced and surveyed,including iterative roots, Schroder’s equation, and iterated equations of polynomial type. The basic contents are listed as follows. Ⅰ.introduction:iteration and related problems;Ⅱ.iterative roots:existence; Ⅲ.iterative roots:uniqueness,differentiability & bifurcation;Ⅳ. iterated equations of polynomial type.