LI Hui,ZHU Xiangyu,TAO Yuanhong*.Frequently convergent solutions of a class of functional difference equation[J].Journal of Yanbian University,2013,39(03):157-160.
一类泛函差分方程的频率收敛解
- Title:
- Frequently convergent solutions of a class of functional difference equation
- 文章编号:
- 1004-4353(2013)03-0157-04
- Keywords:
- frequency measure; difference equation; frequent convergence
- 分类号:
- O177.3
- 文献标志码:
- A
- 摘要:
- 利用数列的频率测度的定义及其性质研究了一类差分方程解的频率收敛性.首先定义与所讨论差分方程密切相关的多项式函数,并求出此函数的不动点; 然后利用此函数在不同区间上的单调性,证明了初始值取在[0,1]区间时,差分方程的解存在两个0.5度频率极限0和1.
- Abstract:
- Frequently convergent solutions of a class of functional difference equation are discussed by using definitions and properties of frequency measure of real valued sequences. First of all, a polynomial function closely related to the difference equation is defined, and then its fixed points are presented. Finally, using monotone properties of this function in different interval, it is proved that if the initial values are in the interval[0,1], then the solutions of the difference equation have two frequent limits 0 and 1 of degree 0.5.
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备注/Memo
收稿日期: 2013-04-13
*通信作者: 陶元红(1973—),女,博士,副教授,研究方向为泛函分析及其应用.
基金项目: 国家自然科学基金资助项目(11361065,11161049); 吉林省自然科学基金资助项目(201215239)