Local Uniform Strong Proximinality of the Space of Continuous Vector-Valued Functions

被引：3

作者：

Indumathi, V. ^{[1
]}

Prakash, N. ^{[1
]}

机构：

[1] Pondicherry Univ, Dept Math, Pondicherry 605014, India

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2017年 / 38卷 / 08期

关键词：

1; 2-ball property; Hausdorff metric continuous; metric projection; proximinal; strongly proximinal; U-proximinal; 46B20; 41A50; 41A65; BANACH-SPACES; SUBSPACES;

D O I：

10.1080/01630563.2017.1296863

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a Banach space, S be a compact Hausdorff space and Y be a U-proximinal subspace of X. We prove that C(S,Y) is locally uniformly strongly proximinal in C(S,X) and the corresponding metric projection map is Hausdorff metric continuous.

引用

页码：1014 / 1023

页数：10

共 11 条

[1]

Dutta S, 2007, CONTEMP MATH, V435, P143

[2] Modulus of Strong Proximinality and Continuity of Metric Projection [J].

Dutta, S. ;

Shunmugaraj, P. .

SET-VALUED AND VARIATIONAL ANALYSIS, 2011, 19 (02) :271-281

[3]

Dutta S., 2017, J CONVEX AN IN PRESS

[4]

Indumathi V., 1997, SEM IN AN, V37

[5] Ball proximinality of equable spaces [J].

Lalithambigai, S. .

COLLECTANEA MATHEMATICA, 2009, 60 (01) :79-88

[6] SUFFICIENT CONDITION FOR PROXIMITY [J].

LAU, KS .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1979, 251 (JUL) :343-356

[7]

LIGHT WA, 1985, LECT NOTES MATH, V1169, pR5

[8] ABSOLUTELY PROXIMAL SUBSPACES OF BANACH-SPACES [J].

MENA, JF ;

PAYA, R ;

RODRIGUEZ, A ;

YOST, DT .

JOURNAL OF APPROXIMATION THEORY, 1991, 65 (01) :46-72

[9] PROXIMINALITY OF CERTAIN SUBSPACES OF CB(S,E) [J].

PROLLA, JB ;

CHIACCHIO, AO .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1989, 19 (01) :335-344

[10] APPROXIMATION BY COMPACT-OPERATORS BETWEEN C(X) SPACES [J].

YOST, D .

JOURNAL OF APPROXIMATION THEORY, 1987, 49 (02) :99-109

← 1 2 →