| 摘要: |
| 主要讨论分式函数的迭代问题.先从研究有理分式出发，用数学归纳法和共轭相似法讨论几类有理线性分式函数f(x)=〖SX(〗x〖〗1+ax〖SX)〗，f(x)=〖SX(〗ax+b〖〗cx+d〖SX)〗，a，b，c，d∈〖WTHZ〗R〖WTBX〗，c(ad-bc)≠0的n次迭代问题，并以此为结论再讨论了几类无理分式f(x)=〖SX(〗x〖〗〖KF(S〗k〖〗1+axk〖KF)〗〖SX)〗，f(x)=〖SX(〗x〖〗1+2a〖KF(〗x〖KF)〗+a2x〖SX)〗，f(x)=〖SX(〗1〖〗〖KF(S〗k〖〗a+bxk〖KF)〗〖SX)〗，a，b∈〖WTHZ〗R〖WTBX〗，k=1，2，3，…的函数迭代，给出了它们的次迭代式. |
| 关键词: 分式函数 迭代 共轭相似 序列 |
| DOI： |
| 分类号: |
| 基金项目: |
|
| Research on Iteration of Several Kinds of Fractional Functions |
|
XIANG Jing jing，JIN Yu guang
|
| Abstract: |
| Mainly on iteration of fractional function，firstly，this paper researches rational fraction discussing some kinds of rational iterative linear fractional functions，such as，f(x)=〖SX(〗x〖〗1+ax〖SX)〗. Based on the conclusion，iteration of irrational fraction，such as，f(x)=〖SX(〗1〖〗〖KF(S〗k〖〗a+bxk〖KF)〗〖SX)〗，and their iterative function are given. |
| Key words: fractional function iteration conjugate similar sequence |
