New generalizations of basic theorems in the KKM theory

被引：18

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

[31] Some generalizations of fixed point theorems and common fixed point theorems [J].

Jang Hyun Jo .

Journal of Fixed Point Theory and Applications, 2018, 20

[32] Some generalizations of fixed point theorems and common fixed point theorems [J].

Jo, Jang Hyun .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2018, 20 (04)

[33] Generalized KKM-type theorems in GFC-spaces and applications [J].

Khanh, Phan Quoc ;

Quan, Nguyen Hong ;

Yao, Jen-Chih .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (3-4) :1227-1234

[34] Fixed-point theorems for multifunctions in S-KKM class [J].

Chang, TH ;

Huang, YY ;

Jeng, JC .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 44 (08) :1007-1017

[35] KKM mappings in cone metric spaces and some fixed point theorems [J].

Turkoglu, Duran ;

Abuloha, Muhib ;

Abdeljawad, Thabet .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (01) :348-353

[36] Two generalizations of some fixed point theorems [J].

Popescu, Ovidiu .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (10) :3912-3919

[37] Generalized G-KKM theorems in generalized convex spaces and their applications [J].

Ding, MP .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 266 (01) :21-37

[38] COMMENTS ON THE KKM THEORY ON HYPERCONVEX METRIC SPACES [J].

Park, Sehie .

TAMKANG JOURNAL OF MATHEMATICS, 2010, 41 (01) :1-14

[39] Elements of the KKM theory on abstract convex spaces [J].

Park, Sehie .

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2008, 45 (01) :1-27

[40] Fixed point theorems for multifunctions having KKM property on almost convex sets [J].

Jeng, JC ;

Hsu, HC ;

Huang, YY .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 319 (01) :187-198

← 1 2 3 4 5 →