FC-空间中的参数型KKM定理及其应用

邓磊; 臧小燕

FC-空间中的参数型KKM定理及其应用

邓磊,
臧小燕

西南大学数学与统计学院,重庆 400715

基金项目: 国家自然科学基金资助项目(10771173);重庆市科委自然科学基金资助项目(CSTC,2005BB2097)

详细信息

作者简介:
邓磊(1957- ),男,重庆人,教授(联系人.Tel:+86-23-68388606;E-mail:dengei@swu.edu.cn).

中图分类号: O177.92
计量
- 文章访问数: 2914
- HTML全文浏览量: 161
- PDF下载量: 674
- 被引次数: 0
出版历程
- 收稿日期: 2007-12-18
- 修回日期: 2008-11-03
- 刊出日期: 2009-01-15

Parametric Type of KKM Theorem in FC-Spaces With Applications

School of Mathematics and Statistics, Southwest University, Chongqing 400715, P. R. China

摘要

摘要: 首先在FC-空间中证明了一个特征性质,然后通过引进线性序空间,利用集合的连通性，在非紧的FC-空间中证明了一个参数型KKM定理．应用参数型KKM定理得到非紧的极大极小不等式、鞍点定理和截口定理．这些结果改进和推广了这个领域中的一些相关结果．
- FC-子空间 /
- FC-参数-拟凸映射 /
- 极大极小不等式
Abstract: First, the authors proved a characteristic property in FC-spaces, then using the connectedness of set, a parametric type of KKM theorem was established in noncompact FC-spaces by introducing a linear ordered space. As consequences, some recent known results such as the noncompact minimax inequalities, saddle point theorem and section theorem were improved. The results improve and generalize the corresponding results in the literature.
- FC-subspace /
- FC-parametric-quasiconvex mapping /
- minimax inequality

HTML全文

参考文献(12)

[1]	Knaster B,Kurnatoaski C,Mazurkiewicz S.Ein beweis des fixpunksatzes fur n-dimensionale simplexe[J].Fund Math,1929,14:132-137.
[2]	Fan Ky. A generalization of Tychonoff′s fixed point theorem[J]. Math Ann,1961,142(3):305-310. doi: 10.1007/BF01353421
[3]	CHANG Shih-sen,CAO Shi-yi,WU Xian.Some nonempty intersection theorems in generalized interval spaces with applications[J].J Math Anal Appl,1996,199(3):787-803. doi: 10.1006/jmaa.1996.0176
[4]	DING Xie-ping.Himmelberg type fixed point theorem in locally FC-spaces[J].J Sichuan Normal University (Natural Science),2005,28(2):127-130.
[5]	DING Xie-ping. Colletive fixed points and a system of coincidence theorems in product FC-spaces and applications[J].Nonlinear Anal,2007,66(11):2604-2617. doi: 10.1016/j.na.2006.03.043
[6]	DING Xie-ping. Maximal element theorems in product FC-spaces and generalized games[J].J Math Anal Appl,2005,305(1):29-42. doi: 10.1016/j.jmaa.2004.10.060
[7]	FANG Min,HUANG Nan-jing. KKM type theorems with applications to generalized vector equilibrium problems in FC-spaces[J].Nonlinear Anal,2007,67(3):809-817. doi: 10.1016/j.na.2006.06.040
[8]	LIN Bor-luh,QUANG Xiu-chi.A non-compact topological minimax theorem[J].J Math Anal Appl,1991,161(2):587-590. doi: 10.1016/0022-247X(91)90353-2
[9]	Stachó L L. Minimax theorems beyond topological vector spaces[J].Acta Sci Math,1980,42(1/2):157-164.
[10]	CHENG Cao-zong, LIN You-hao.On the generalization of minimax theorem for the type of fixed points[J].Acta Math Sinica,1991,34(4):502-507.
[11]	Komornik V. Minimax theorems for upper semi-continuous fuctions[J].Acta Math Acad Sci Hungar,1982,40(7):159-163. doi: 10.1007/BF01897316
[12]	TIAN Guo-qiang. Generalization of the FKKM theorem and the Ky Fan minimax inquality,with applications to maximal elements,price equilibrium,and complementarity[J].J Math Anal Appl,1992,170(2):457-471. doi: 10.1016/0022-247X(92)90030-H