Parametric Type of KKM Theorem in FC-Spaces With Applications

DENG Lei; ZANG Xiao-yan

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DENG Lei, ZANG Xiao-yan. Parametric Type of KKM Theorem in FC-Spaces With Applications[J]. Applied Mathematics and Mechanics, 2009, 30(1): 75-82.

Citation:

DENG Lei, ZANG Xiao-yan. Parametric Type of KKM Theorem in FC-Spaces With Applications[J]. Applied Mathematics and Mechanics, 2009, 30(1): 75-82.

Citation:

DENG Lei, ZANG Xiao-yan. Parametric Type of KKM Theorem in FC-Spaces With Applications[J]. Applied Mathematics and Mechanics, 2009, 30(1): 75-82.

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Parametric Type of KKM Theorem in FC-Spaces With Applications

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

Received Date: 2007-12-18
Rev Recd Date: 2008-11-03
Publish Date: 2009-01-15

Abstract

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

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References(12)

References

[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