Modulus of Strong Proximinality and Continuity of Metric Projection

被引：4

作者：

Dutta, S. ^{[1
]}

Shunmugaraj, P. ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2011年 / 19卷 / 02期

关键词：

Strong proximinality; Metric projections; Modulus of strong proximinality; Hausdorff metric continuous; BANACH-SPACES; SUBSPACES;

D O I：

10.1007/s11228-010-0143-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we initiate a quantitative study of strong proximinality. We define a quantity I mu(x, t) which we call as modulus of strong proximinality and show that the metric projection onto a strongly proximinal subspace Y of a Banach space X is continuous at x if and only if epsilon(x, t) is continuous at x whenever t > 0. The best possible estimate of epsilon(x, t) characterizes spaces with 1 1/2 ball property. Estimates of epsilon(x, t) are obtained for subspaces of uniformly convex spaces and of strongly proximinal subspaces of finite codimension in C(K).

引用

页码：271 / 281

页数：11