Closed convex sets and their best simultaneous approximation properties with applications

被引：3
|
作者：
Mohebi, H. [1 ]
Naraghirad, E. [1 ]
机构：
[1] Univ Kerman, Mahani Math Res Ctr, Kerman, Iran
来源：
OPTIMIZATION LETTERS | 2007年 / 1卷 / 04期
关键词：
Simultaneous best approximation; Simultaneous pseudo-Chebyshev set; Simultaneous quasi-Chebyshev set; Conditionally complete lattice Banach space; Extremal point;
D O I：
10.1007/s11590-006-0017-2
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
We develop a theory of best simultaneous approximation for closed convex sets in a conditionally complete lattice Banach space X with a strong unit. We study best simultaneous approximation in X by elements of closed convex sets, and give necessary and sufficient conditions for the uniqueness of best simultaneous approximation. We give a characterization of simultaneous pseudo-Chebyshev and quasi-Chebyshev closed convex sets in X. Also, we present various characterizations of best simultaneous approximation of elements by closed convex sets in terms of the extremal points of the closed unit ball B-X* of X*.
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页码：313 / 328
页数：16
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