粗I-收敛点集的严格凸性  

The strict convexity of set defined by rough I-convergent points

作　　者：施慧华 SHI Huihua(School of Mathematical Science,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学数学科学院,福建泉州362021

出　　处：《厦门大学学报（自然科学版）》2020年第3期441-444,共4页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11401227)。

摘　　要：设r≥0,称赋范空间X中的序列{x n}是粗I-收敛(亦记r-I-收敛)的,若I-LIM r x n={x∈X:I-lim n→∞sup‖x n-x‖≤r}是非空集合,对具有可加性质的理想I,证明了当X是一致凸时,I-LIM r x n是严格凸的,并分别讨论了{x n}的粗I-聚点与粗I-极限点、粗I-聚点与I-聚点之间的关系.A sequence{x n}in a normed space X is said to be r-I-convergent for some r≥0,if the set defined by I-LIM r x n={x∈X:I-lim n→∞sup‖x n-x‖≤r}is non-empty.In this paper,we prove that,if an ideal I features an additive property and X is uniformly convex,I-LIM r x n is strictly convex.Furthermore,we present the relationship between r-I-cluster points and r-I-limit points,r-I-cluster points and I-cluster points.

关 键 词：粗I-收敛 I-上极限 严格凸性 粗I-聚点 

分 类 号：O177[理学—数学]