理想收敛的若干研究及推广  

Some Discussions and Generalizations of Ideal Convergence

作　　者：施慧华[1] 王波[1] 

机构地区：[1]华侨大学数学科学学院,泉州362021

出　　处：《数学学报（中文版）》2016年第3期335-342,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(11226129;11201160;11401227);福建省自然科学基金(2012J05006)资助项目

摘　　要：在Banach空间X中利用序列的I-收敛与I*-收敛给出理想I具可加性质(AP)的等价刻画,并进一步研究弱I-收敛、弱I*-收敛、一致弱I*-收敛之间,以及弱I-收敛与收敛之间的关系,最后基于I-λ-统计收敛给出其推广:I-A-统计收敛,并以次微分映射为工具定义一族有限可加测度,用于等价刻画I-A-统计收敛,这亦是有限可加测度的一个应用体现.Applying I-convergence and I＊-convergence of sequences in Banach space X, this paper first present a sufficient and neccessary condition for an ideal I has the ad- ditive property, then establish the relation between w-I-convergence, w-I＊-convergnence and uni-w-I＊-convergence, also the connection between w-I-convergence and Conver- gence, finally we define/-A-statistical convergence which is the generalization of I-A- statistical convergence, and by using subdifferential mapping to define a set of finite additive measures, we show the equivalent description of I-A-statistical convergence, this is an application of finite additive measures.

关 键 词：I-收敛 I＊-收敛 I-A-统计收敛 

分 类 号：O177.92[理学—数学]