Generalized Vector Variational-Type Inequalities in FC-Spaces
-
摘要: 在FC-空间中引入和研究了一类广义向量变分型不等式(GVVTIP),包含了大多数向量平衡问题,向量变分不等式问题,广义向量平衡问题和广义向量变分不等式问题作为特殊情况.利用F-KKM定理,在非紧FC-空间中,建立了关于GVVTIP解的某些新的存在定理.这些定理统一、改进和推广了文献中的一些重要的已知结果.
-
关键词:
- 广义向量变分型不等式 /
- F-KKM映射 /
- F-Px-对角拟凸 /
- FC-空间
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. -
[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,Schlger 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]. Cx-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.
点击查看大图
计量
- 文章访问数: 2152
- HTML全文浏览量: 47
- PDF下载量: 736
- 被引次数: 0