变系数多项式型迭代函数方程的连续周期解  

PERIODIC AND CONTINUOUS SOLUTIONS FOR POLYNOMIAL-LIKE ITERATIVE FUNCTIONAL EQUATION WITH VARIABLE COEFFICIENTS

作　　者：颜东燕 赵侯宇 YAN Dong-yan;ZHAO Hou-yu(School of Mathematics,Chongqing NormalUniversity,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《数学杂志》2021年第5期377-383,共7页Journal of Mathematics

基　　金：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)。

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λ_(1)(x)f(x)+λ_(2)(x)f^(2)(x)+...+λn(x)f^(n)(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.Schauder’s fixed point theorem and the Banach contraction principle are used to study the polynomial-like iterative functional equation with variable coefficientsλ_(1)(x)f(x)+λ_(2)(x)f^(2)(x)+...+λn(x)f^(n)(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.

关 键 词：迭代函数方程 周期解 不动点定理 

分 类 号：O175[理学—数学] O178[理学—基础数学]