多元函数列的一致收敛性及相关极限性质的研究  

Uniform Convergence of Multivariate Function Sequences and Its Limit Properties

作　　者：费时龙[1] 洪佳音 朱少娟 Fei Shilong;Hong Jiayin;Zhu Shaojuan(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 [2]宿州学院,安徽宿州234000

出　　处：《廊坊师范学院学报（自然科学版）》2020年第2期8-10,共3页Journal of Langfang Normal University(Natural Science Edition)

基　　金：安徽省高等学校省级自然科学基金资助项目(KJ2016A770);安徽省高校优秀青年人才支持计划重点项目(gxyqZD2016340);省级大学生创新创业项目(201810379095)。

摘　　要：在一元函数列一致收敛及其极限性质的基础上定义了二元函数列及多元函数列一致收敛的概念。给出了二元函数列及多元函数列一致收敛的柯西收敛准则判别法,得到了其一致收敛的几个充要条件,并分别研究了二元函数列及多元函数列一致收敛极限函数的连续性、可微性及可积性,获得了一致收敛极限函数一致连续的充分条件。The concept of uniform convergence of binary function columns and multivariate function columns is defined on the basis of uniform convergence of one element function column and its limit properties,giving the method of uniform convergence for multivariate function sequences.The paper gives the Cauchy convergence criterion of uniform convergence of binary function columns and multivariate function columns and the conditions of their uniform convergence.The continuity,differentiability and integrability of uniformly convergent limit functions are studied respectively,and the uniform continuity of uniformly convergent limit functions is discussed.

关 键 词：多元函数列 一致收敛 一致连续 连续可微 可积 

分 类 号：O172[理学—数学]