The locally k-uniformly extremely convex and midpoint locally k-uniformly extremely convex Banach spaces

被引：0

作者：

Wulede, Suyalatu ^{[1
]}

机构：

[1] Inner Mongolia Normal Univ, Coll Math Sci, Hohhot 010022, Peoples R China

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2021年 / 52卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Banach space; Locally k-uniformly extremely convex space; Midpoint locally k-uniformly convex space; ROTUND;

D O I：

10.1007/s13226-021-00053-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The locally k-uniformly extremely convex Banach spaces are introduced. It is shown here that every locally k-uniformly extremely convex space is locally (k+1)-uniformly extremely convex space, but the converse implication is not true. Some properties of locally k-uniformly extremely convex spaces are given. Specially, it is proved that if the second dual of Banach space X is locally 2-uniformly extremely convex, then X is reflexive. In addition, the notion of midpoint locally k-uniformly extreme convexity is introduced and its relations to other type convexity are given.

引用

页码：512 / 520

页数：9

共 21 条

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