New generalizations of basic theorems in the KKM theory

被引：17

作者：

Park, Sehie ^{[1
,2
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[2] Natl Acad Sci, Seoul 137044, South Korea

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 09期

关键词：

Intersectionally closed; Unionly open; Abstract convex space; Geometric lemma; Fixed point; Maximal element; Minimax inequality; Variational inequality; MAXIMAL ELEMENTS; FOUNDATIONS; SETS;

D O I：

10.1016/j.na.2011.01.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we obtain a new KKM type theorem for intersectionally closed-valued KKM maps and some useful new basic consequences. Typical examples of them are abstract forms of Fan's matching theorem, Fan's geometric lemma, the Fan-Browder fixed point theorem, maximal element theorems, Fan's minimax inequality, variational inequalities, and others. (c) 2011 Elsevier Ltd. All rights reserved.

引用

页码：3000 / 3010

页数：11

共 50 条

[1] Applications of some basic theorems in the KKM theory
Sehie Park
[J]. Fixed Point Theory and Applications, 2011
[2] Applications of some basic theorems in the KKM theory
Park, Sehie
[J]. FIXED POINT THEORY AND APPLICATIONS, 2011,
[3] Generalizations of the KKM type theorems on generalized convex spaces
Park, S
Kim, H
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1998, 29 (02): : 121 - 132
[4] Generalizations of the nash equilibrium theorem in the KKM theory
Park S.
[J]. Fixed Point Theory and Applications, 2010 (1)
[5] Basic theorems on multimaps of the KKM, Browder and Kakutani types
Park, S
[J]. FIXED POINT THEORY AND APPLICATIONS, VOL 5, 2004, : 109 - 117
[6] A UNIFIED APPROACH TO GENERALIZATIONS OF THE KKM-TYPE THEOREMS RELATED TO ACYCLIC MAPS
PARK, S
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1994, 15 (1-2) : 105 - 119
[7] Remarks on some basic concepts in the KKM theory
Park, Sehie
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (07) : 2439 - 2447
[8] New proof of basic theorems in theory of matrix
Bao, Xueyou
Liu, Huidi
[J]. Harbin Gongye Daxue Xuebao/Journal of Harbin Institute of Technology, 27 (01):
[9] NEW GENERALIZATIONS OF AN H-KKM TYPE THEOREM AND THEIR APPLICATIONS
DING, XP
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1993, 48 (03) : 451 - 464
[10] NEW FOUNDATIONS OF THE KKM THEORY
Park, Sehie
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2008, 9 (03) : 331 - 350

← 1 2 3 4 5 →