PDF(462 KB)
PDF(462 KB)
PDF(462 KB)
理想收敛的若干研究及推广
Some Discussions and Generalizations of Ideal Convergence
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 additive 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 convergence,finally we define I-A-statistical convergence which is the generalization of I-λ-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.
I-收敛 / I*-收敛 / I-A-统计收敛 {{custom_keyword}} /
I-convergence / I*-convergence / I-A-statistical convergence {{custom_keyword}} /
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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
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