一致收敛二元函数列及函数项级数的含参量积分性质  

The Parametric Integral Properties of Limit Functions of Uniformly Convergent Binary Function Sequences and Series of Function Items

作　　者：费时龙[1] 任雅柔 FEI Shilong;REN Yarou(School of Mathematics and Statistics,Suzhou University,Suzhou 234000,China)

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《吉林化工学院学报》2023年第1期95-98,共4页Journal of Jilin Institute of Chemical Technology

基　　金：安徽省高等学校省级自然科学基金资助项目(KJ2016 A770);安徽省高校优秀青年人才支持计划重点项目(gxyqZD2016340);宿州学院科研发展基金项目(2021fzjj15)。

摘　　要：目的是利用二元函数列的性质研究其极限函数及二元函数项级数的含参量积分的相关性质。通过二元函数列的含参量积分存在性、连续性、可微性及可积性研究了一致收敛的极限函数及函数项级数和函数对应的含参量积分的存在性、连续性、可微性与可积性。获得了一致收敛意义下极限函数对应的含参量积分与极限交换次序、求导交换次序及累次积分交换次序的条件,得到了一致收敛意义下含参量积分与无穷求和交换次序,含参量积分的求导与无穷求和交换次序的条件。The main purpose of this paper is to study the properties of parametric integrals about limit functions and series of binary function by using the properties of series of binary function.The existence,the continuity,differentiability and integrability of parametric integrals corresponding to uniformly convergent limit functions and the series of function items were studied through the existence,the continuity,differentiability and integrability of parametric integrals of binary function sequences.We obtained the conditions of the exchange order of parametric integrals about limit function and the limit order,derivative and the cumulative integral in the sence of uniformly convergence.At last,the conditions that exchange order of parametric integrals and infinite sum and derivative were obtained.

关 键 词：一致收敛 含参量积分 二元函数列 极限函数 函数项级数 和函数 

分 类 号：O172[理学—数学]