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
收藏
页码：119 / 131
页数：13
相关论文
共 50 条
  • [21] SOME REMARKS ON THE VISIBLE POINTS OF A LATTICE
    BAAKE, M
    GRIMM, U
    WARRINGTON, DH
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1994, 27 (08): : 2669 - 2674
  • [22] Some remarks on rational periodic points
    Kawaguchi, S
    MATHEMATICAL RESEARCH LETTERS, 1999, 6 (5-6) : 495 - 509
  • [23] The Farthest and the Nearest Points of Sets
    Balashov, Maxim V.
    Ivanov, Grigorii E.
    JOURNAL OF CONVEX ANALYSIS, 2018, 25 (03) : 1019 - 1031
  • [24] Farthest points on convex surfaces
    Zamfirescu, T
    MATHEMATISCHE ZEITSCHRIFT, 1997, 226 (04) : 623 - 630
  • [25] Quasigeodesics and farthest points on convex surfaces
    Ieiri, K.
    Itoh, J.
    Vilcu, C.
    ADVANCES IN GEOMETRY, 2011, 11 (04) : 571 - 584
  • [26] Multiple farthest points on Alexandrov surfaces
    Vilcu, Costin
    Zamfirescu, Tudor
    ADVANCES IN GEOMETRY, 2007, 7 (01) : 83 - 100
  • [27] Existence of farthest points in Hilbert spaces
    Tehrani, Hamid Mazaheri
    Jafarbeigi, Raham Rahmani
    INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2021, 12 (02): : 437 - 446
  • [28] Criteria for farthest points on convex surfaces
    Itoh, Jin-ichi
    Vilcu, Costin
    MATHEMATISCHE NACHRICHTEN, 2009, 282 (11) : 1537 - 1547
  • [29] Some remarks on best approximation and fixed points
    Delbosco, D
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1999, 30 (08): : 745 - 748
  • [30] Remarks on some points in the treatment of nerve injuries
    Sherren, J
    BMJ-BRITISH MEDICAL JOURNAL, 1910, 1910 : 130 - 131
12345