Generalized Vector Variational-Type Inequalities in FC-Spaces

FANG Min; DING Xie-ping

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FANG Min, DING Xie-ping. Generalized Vector Variational-Type Inequalities in FC-Spaces[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1271-1279.

Citation:

FANG Min, DING Xie-ping. Generalized Vector Variational-Type Inequalities in FC-Spaces[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1271-1279.

Citation:

FANG Min, DING Xie-ping. Generalized Vector Variational-Type Inequalities in FC-Spaces[J]. Applied Mathematics and Mechanics, 2006, 27(11): 1271-1279.

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Generalized Vector Variational-Type Inequalities in FC-Spaces

FANG Min¹,
DING Xie-ping²

1.
College of Mathematics, Sichuan University, Chengdu 610064, P. R. China;
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China

Received Date: 2005-11-01
Rev Recd Date: 2006-08-06
Publish Date: 2006-11-15

Abstract

Abstract

A class of generalized vector variational-type inequality problems(in short,GVVTIP)are studied in FC-spaces,which include most of vector equilibrium problems,vector variational inequality problems,generalized vector equilibrium problems and generalized vector variational inequality problem as special cases.By using F-KKM theorem,some new existence results for GVVTIP are established in noncompact FC-space.As consequences,some recent known results in literature are obtained under much weaker assumption.
- generalized vector variational-type inequality,
- F-KKM mapping,
- F-P_x-diagonally quasiconvex,
- FC-space

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References(21)

References

[1]	Giannessi F.Theorems of alternative, quadratic programs and complementary problems[A].In:Cottle R W,Giannessi F,Lions J L,Eds.Variational Inequalities and Complementarity Problems[C].New York:John Wiley Sons,1980，151—186.
[2]	Song W.Vector equilibrium problems with set-valued mappings[A].In:Giannessi F,Ed.Vector Variational Inequalities and Vector Equilibria[C].London:Kluwer Acad Pub,2000,403—422.
[3]	Lin L J,Park S.On some generalized quasi-equilibrium problem[J].J Math Anal Appl,1998,224[STBZ]. (2):167—181.
[4]	Ansari Q H,Yao J C.An existence result for the generalized vector equilibrium problem[J].Appl Math Lett,1999,12[STBZ]. (8):53—56.
[5]	Oettli W，Schlger D.Existence of equilibrium for g-monotone mappings[A].In:Takahashi W,Tanaka T,Eds.Nonlinear Analysis and Convex Analysis[C].Singapore：World Sci Pub,1999,26—33.
[6]	DING Xie-ping,Tarafdar E.Generalized vector variational-like inequalities with[WT5”BZ]. Cx-η-[WT5”B4]. pseudomontone set-valued mappings[A].In:Giannessi F,Ed.Vector Variational Inequalities and Vector Equilibria[C].London:Kluwer Acad Pub,2000,125—140.
[7]	DING Xie-ping.The generalized vector quasi-variational-like inequalities[J].Computers Math Appl,1999,37(6)：57—67.
[8]	DING Xie-ping,Park J Y.Generalized vector equilibrium problems in generalized convex spaces[J].J Optim Theory Appl,2004,120[STBZ]. (2):327—353.
[9]	DING Xie-ping,Park J Y.Fixed points and generalized vector equilibrium problems in generalized convex spaces[J].Indian J Pure Appl Math,2003,34[STBZ]. (6):973—990.
[10]	DING Xie-ping.Generalized R-KKM type theorems in topological spaces and application[J].四川师范大学学报,2005,28[STBZ]. (5):505—513.
[11]	Ansari Q H,Siddiqi A H,Yao J C.Generalized vector variational-like inequalities and their scalarizations[A].In:Giannessi F,Ed.Vector Variational Inequalities and Vector Equlibria[C].London:Kluwer Acad Pub,2000,17—37.
[12]	DING Xie-ping,Tarafdar E.Generalized vector variational-like inequalities without monotonicity[A].In:Giannessi F,Ed.Vector Variational Inequalities and Vector Equilibria[C].London:Kluwer Acad Pub,2000,113—124.
[13]	Chang S S,Thompson H B，Yuan G X Z.Existence of solutions for generalized vector variational-like inequalities[A].In:Giannessi F, Ed.Vector Variational Inequalities and Vector Equilibria[C].London:Kluwer Acad Pub,2000,39—53.
[14]	Luo Q.Generalized vector variational-like inequalities[A].In:Giannessi F,Ed.Vector Variational Inequalities and Vector Equilibria[C].London:Kluwer Acad Pub,2000,363—369.
[15]	Giannessi F.Vector Variational Inequalities and Vector Equilibria[M].London:Kluwer Acad Pub,2000.
[16]	Lee B S，Lee S J.Vector variational-type inequalities for set-valued mappings[J].Appl Math Lett,2000,13(3)：57—62.
[17]	DING Xie-ping.Maximal elements theorems in product FC-space and generalized games[J].J Math Anal Appl,2005,305(1)：29—42. doi: 10.1016/j.jmaa.2004.10.060
[18]	DING Xie-ping.Generalized G-KKM theorems in generalized convex space and their applications[J].J Math Anal Appl,2002,266[STBZ]. (1):21—37.
[19]	Deng L，Xia X.Generalized R-KKM theorems in topological space and their application[J].J Math Anal Appl,2003,285[STBZ]. (2):679—690.
[20]	Aubin J P，Ekeland I.Applied Nonlinear Analysis[M].New York:John Wiley Sons,1984.
[21]	Klein E,Thompson A C.Theory of Correspondences[M].New York:John Wiley Sons,1984.