等度收敛函数列的性质与应用

Properties and Application of Equidegree Convergent Function Sequence

一致收敛函数列是数学分析研究的重点与难点,而其中的等度一致连续函数列更是众多学者研究的热点。等度收敛函数列则是模仿等度一致连续函数列的定义而定义的。文章通过探究等度收敛函数列的性质与应用,得出函数列等度收敛的条件强于一致收敛的条件,找到能移植到等度收敛函数列中的一致收敛函数列的性质,并列出该性质的证明过程,同时呈现等度收敛函数列在常微分方程中的应用。

Uniformly convergent function sequence is the focus and difficulty of mathematical analysis,and the equidegree uniformly continuous function sequence is the focus of many scholars.The equidegree convergent function sequence is defined by imitating the definition of equidegree uniformly continuous function sequence.By exploring the properties and applications of equidegree convergence function sequence,this paper obtains that the condition of equidegree convergence of function sequence is stronger than that of uniform convergence,finds the property of uniform convergence function sequence that can be transplanted into equidegree convergence function sequence,lists the proof process of this property,and presents the application of equidegree convergence function sequence in ordinary differential equations.