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| 摘要: |
| 本文利用Schauder’s不动点定理和Banach压缩映像原理讨论了一类变系数多项式型迭代函数方程λ1（x）f（x）+λ2（x）f2（x）+...+λn（x）fn（x）=F（x），得到了此类方程的连续周期解的存在性、唯一性和稳定性的结论，并通过几个例子验证了所得定理的正确性.所得结果丰富和推广了多项式型迭代函数方程的相关理论. |
| 关键词: 迭代函数方程 周期解 不动点定理 |
| DOI： |
| 分类号:O175;O178 |
| 基金项目:Supported by the Foundation of Chongqing Municipal Education Commission (KJQN201800502; KJQN201900525); Foundation of youth talent of Chongqing Normal University (02030307-00039); Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX0857). |
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| PERIODIC AND CONTINUOUS SOLUTIONS FOR POLYNOMIAL-LIKE ITERATIVE FUNCTIONAL EQUATION WITH VARIABLE COEFFICIENTS |
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YAN Dong-yan,ZHAO Hou-yu
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| Abstract: |
| Schauder's fixed point theorem and the Banach contraction principle are used to study the polynomial-like iterative functional equation with variable coefficients λ1(x)f(x) + λ2(x)f2(x) +... + λn(x)fn(x)=F(x). We give sufficient conditions for the existence, uniqueness, and stability of the periodic and continuous solutions. Finally, some examples were considered by our results. The results enrich and extend the theory about polynomial-like iterative functional equation. |
| Key words: Iterative functional equation periodic solutions fixed point theorem |
