Some remarks on farthest points

被引：2

作者：

Montesinos, Vicente ^{[1
]}

Zizler, Peter ^{[2
]}

Zizler, Vaclav ^{[3
]}

机构：

[1] Univ Politecn Valencia, Inst Matemat Pura & Aplicada, Valencia 46022, Spain

[2] Mt Royal Univ, Dept Math Phys & Engn, Calgary, AB, Canada

[3] Acad Sci Czech Republ, Inst Math, CR-11567 Prague 1, Czech Republic

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2011年 / 105卷 / 01期

关键词：

Farthest points; Strongly exposed points; Generic differentiability; Convex functions; UNIFORMLY CONVEX;

D O I：

10.1007/s13398-011-0012-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We use renormings and generic differentiability of convex functions to prove some results on farthest points in sets in Banach spaces. As a corollary, we obtain an alternative proof of the Lindenstrauss-Troyanski result on representation of weakly compact convex sets by means of strongly exposed points. We use this approach to simplify former proofs of several known results in this area.

引用

页码：119 / 131

页数：13

共 50 条

[1] Some remarks on farthest points
Vicente Montesinos
Peter Zizler
Václav Zizler
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2011, 105 : 119 - 131
[2] Farthest points and the farthest distance map
Bandyopadhyay, P
Dutta, S
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2005, 71 (03) : 425 - 433
[3] Characterizations of Some Rotundity Properties in Terms of Farthest Points
Prasath, C. Arunachala
Thota, Vamsinadh
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2025, 22 (02)
[4] REMARKS ON THE UNIQUE FARTHEST POINT PROBLEM IN SOME SUBSPACES OF C
BOSZNAY, AP
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1981, 37 (04): : 471 - 479
[5] FARTHEST POINTS OF SETS
PANDA, BB
KAPOOR, OP
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1978, 62 (02) : 345 - 353
[6] On farthest points of sets
Balashov, M. V.
Ivanov, G. E.
MATHEMATICAL NOTES, 2006, 80 (1-2) : 159 - 166
[7] FARTHEST POINTS AND POROSITY
Boulos, Wissam
Reich, Simeon
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2014, 15 (06) : 1319 - 1329
[8] Farthest points and cut loci on some degenerate convex surfaces
Itoh J.-I.
Vîlcu C.
Journal of Geometry, 2004, 80 (1-2) : 106 - 120
[9] ON EXISTENCE OF FARTHEST POINTS
PANDA, BB
DWIVEDI, K
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1985, 16 (05): : 486 - 490
[10] On farthest points of sets
M. V. Balashov
G. E. Ivanov
Mathematical Notes, 2006, 80 : 159 - 166

← 1 2 3 4 5 →