A remark on intersection of convex sets

被引：2

作者：

Marino, G ^{[1
]}

机构：

[1] Univ Calabria, Dept Math, I-87036 Arcavacata Di Rende, CS, Italy

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2003年 / 284卷 / 02期

关键词：

convex sets; neighborhood; inward set; pseudo-contractive map;

D O I：

10.1016/S0022-247X(03)00330-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a real Banach space. Let {G(gamma): gamma is an element of Gamma} be a family of closed, convex subsets of X. We show that either the intersection boolean AND(gammais an element ofGamma) (G(gamma))(epsilon) of the epsilon-neighborhood of the sets G(gamma) is bounded for each epsilon>0, or it is unbounded for each epsilon>0. From this we derive a fixed point theorem for suitable maps that move some points along a bounded direction in Hilbert spaces. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：775 / 778

页数：4

共 50 条

[21] SOME INTERSECTION AND GENERATION PROPERTIES OF CONVEX-SETS
JAMISON, RE
COMPOSITIO MATHEMATICA, 1977, 35 (02) : 147 - 161
[22] On the chromatic number of intersection graphs of convex sets in the plane
Kim, SJ
Kostochka, A
Nakprasit, K
ELECTRONIC JOURNAL OF COMBINATORICS, 2004, 11 (01):
[23] Distributed Asynchronous Projection onto the Intersection of Convex Sets
Fioravanti, Camilla
Oliva, Gabriele
Panzieri, Stefano
2022 30TH MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION (MED), 2022, : 37 - 42
[24] Intersection Theorems for Infinite Families of Convex Sets in Graphs
Norbert Polat
Periodica Mathematica Hungarica, 1997, 35 (1-2) : 95 - 108
[25] Remark on Zero Sets of Holomorphic Functions in Convex Domains of Finite Type
Jasiczak, Michal
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2010, 53 (02): : 311 - 320
[26] FAMILIES OF CONVEX-SETS HAVING THE CONSTANT INTERSECTION PROPERTY
COQUET, G
DUPIN, JC
ARCHIV DER MATHEMATIK, 1979, 33 (02) : 172 - 176
[27] THEOREM ON NONEMPTY INTERSECTION OF CONVEX-SETS AND ITS APPLICATION
ANDO, T
JOURNAL OF APPROXIMATION THEORY, 1975, 13 (02) : 158 - 166
[28] MAZURS INTERSECTION PROPERTY OF BALLS FOR COMPACT CONVEX-SETS
WHITFIELD, JHM
ZIZLER, V
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1987, 35 (02) : 267 - 274
[29] Mazur intersection properties for compact and weakly compact convex sets
Vanderwerff, J
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1998, 41 (02): : 225 - 230
[30] A REMARK ON INTERSECTION OF SHELLS
STILES, WJ
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 19 (04) : 831 - +

← 1 2 3 4 5 →