| 拟线性迭代函数方程的解析解 |
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| 引用本文： | 袁放,陈玉会. 拟线性迭代函数方程的解析解[J]. 淮阴工学院学报, 2008, 17(5): 34-39 |
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| 作者姓名： | 袁放 陈玉会 |
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| 作者单位： | 淮安市广播电视大学,江苏,淮安,223003 |
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| 摘 要： | 研究讨论关于拟线性迭代甬数方程λ1（f（z））f（z）＋λ2（f（z））f^2（z）＋…＋λn（f（z））f^n（z）=F（z）解析式的存在唯一性。通过Schroder变换，以上迭代方程能被转化为一个不含有未知函数迭代的辅助函数方程。因此通过有限阶非线性函数方程系的已知结果可以得到关于拟线性迭代函数方程的解析解。
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| 关 键 词： | 拟线性 迭代函数方程 解析解 局部解析解 |
Analytic Solutions of a Quasi-linear Iterative Functional Equation |
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| YUAN Fang,CHEN Yu-hui. Analytic Solutions of a Quasi-linear Iterative Functional Equation[J]. Journal of Huaiyin Institute of Technology, 2008, 17(5): 34-39 |
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| Authors: | YUAN Fang CHEN Yu-hui |
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| Affiliation: | Huai'an Television University;Huai'an Jiangsu 223003;China |
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| Abstract: | In this paper, existence uniqueness of analytic solutions to a quasi - linear iterative functional equation λ1 （f（z））f（z） ＋ λ2（f（z） ）f^2（z） ＋ … ＋ λn（f（z） ）f^n（z） = F（z） is studied. By applying Schroder transformation, the above iterative equation can be reduced to an auxiliary functional equation which does not include the iteration of unknown function. As a result, analytic solutions of the quasi - linear iterative functional equations are obtained by applying known results of systems of nonlinear functional equations of finite orders. |
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| Keywords: | quasi-linear iterative functional analytic solutions local analytic solutions |
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