Periodic and continuous solutions of a polynomial-like iterative equation

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• 作者：Che Tat Ng ; Hou Yu Zhao
• 关键词：Iterative functional equation ; periodic solutions ; fixed point theorem
• 刊名：Aequationes mathematicae
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：91
• 期：1
• 页码：185-200
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Combinatorics;
• 出版者：Springer International Publishing
• ISSN：1420-8903
• 卷排序：91

文摘

Schauder’s fixed point theorem and the Banach contraction principle are used to study the polynomial-like iterative functional equation $$\begin{aligned} \lambda _1f(x)+\lambda _2f^2(x)+\cdots +\lambda _n f^n(x)=F(x). \end{aligned}$$We give sufficient conditions for the existence, uniqueness, and stability of the periodic and continuous solutions. We examine the monotonicity, convexity, and differentiability of the solutions of the family \(2f(x)+\lambda f^2(x)=\sin (x)\), (\(\lambda \in [0,1]\)).KeywordsIterative functional equationperiodic solutionsfixed point theoremThis work was partially supported by the National Natural Science Foundation of China (Grant No. 11326120, 11501069), Foundation of Chongqing Municipal Education Commission (Grant No. KJ1400528, KJ1600320).