BREGMAN DISTANCES AND KLEE SETS IN BANACH SPACES

被引：1

作者：

Fang, Donghui ^{[1
,2
]}

Song, Wen ^{[3
]}

Li, Chong

机构：

[1] Jishou Univ, Sch Math & Comp Sci, Jishou 416000, Peoples R China

[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

[3] Harbin Normal Univ, Sch Math Sci, Harbin 150025, Peoples R China

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2009年 / 13卷 / 6A期

关键词：

Bregman farthest-point map; Klee set; D-maximally approximate compactness; Totally convex function; MONOTONE-OPERATORS; CONVEX-FUNCTIONS; FARTHEST POINTS; CHEBYSHEV SETS; OPTIMIZATION; PROJECTIONS; ALGORITHMS;

D O I：

10.11650/twjm/1500405617

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we first present some sufficient conditions for the upper semicontinuity and/or the continuity of the Bregman farthest-point map Q(C)(g) and the relative farthest-point map S-C(g) for a nonempty D-maximally approximately compact subset C of a Banach space X. We next present certain sufficient conditions as well as equivalent conditions for a Klee set to be singleton in a Banach space X. Our results extend and/or improve the corresponding ones of [Bauschke, et al., J. Approx. Theory, 158 (2009), pp. 170-183] to infinite dimensional spaces.

引用

页码：1847 / 1865

页数：19

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