乘积G-凸空间内的非空交定理和广义矢量平衡问题组

丁协平

乘积G-凸空间内的非空交定理和广义矢量平衡问题组

丁协平

四川师范大学数学与软件科学学院,成都 610066

基金项目: 国家自然科学基金资助项目(19871059);四川省教育厅重点研究基金资助项目([2000]25)

详细信息

作者简介:
丁协平(1938- ),男,四川自贡人,教授(Tel:+86-28-84760929;E-mail:dingxip@sicnu.edu.cn).

中图分类号: O177.92;O225
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- 文章访问数: 2560
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- 被引次数: 0
出版历程
- 收稿日期: 2002-08-29
- 修回日期: 2003-12-05
- 刊出日期: 2004-06-15

Nonempty Intersection Theorems and System of Generalized Vector Equilibrium Problems in Product G-Convex Spaces

DING Xie-ping

Department of Mathematics, Sichuan Normal University, Chengdu 610066, P. R. China

摘要

摘要: 利用作者在G-凸空间内对集值映象簇得到的一个极大元存在性定理，在非紧乘积G-空间内，对集值映象簇建立了某些新的非空交定理．作为应用，在非紧乘积G-凸空间内，对广义矢量平衡问题组证明了一些平衡存在性定理．这些定理统一、改进和推广了文献中一些重要的已知结果．
- 集值映象组 /
- 非空交定理 /
- 广义矢量平衡问题组 /
- 乘积G-凸空间
Abstract: By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.
- family of set-valued mapping /
- nonempty intersection theorem /
- system of generalized vector equilibrium problem /
- product G-convex space

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参考文献(23)

[1]	Giannessi F. Theorems of alternative, quadratic programs and complementarity problems[A].In:R W Cottle, F Giannessi,J -L Lions Eds.Variational Inequalities and Complementarity Problems[C].New York:J Wiley Sons,1980,151—186.
[2]	Giannessi F.Vector Variational Inequalities and Vector Equilibria Mathematics Theories[M].London:Kluwer Academic Publishers,2000.
[3]	Pang J S.Asymmetric variational inequality problems over product sets: applications and iterative methods[J].Math Programming,1985，31(2):206—219. doi: 10.1007/BF02591749
[4]	Zhu D L, Marcotte P. Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities[J].SIAM J Optim,1996，6(3)：714—726. doi: 10.1137/S1052623494250415
[5]	Cohen G, Chaplais F. Nested monotony for variational inequalities over product of spaces and convergence of iterative algorithms[J]. J Optim Theory Appl,1988,59(2):360—390.
[6]	Ansari Q H, Yao J C. A fixed point theorem and its applications to a system of variational inequalities[J].Bull Austral Math Soc,1999,59(2):433—442. doi: 10.1017/S0004972700033116
[7]	Ansari Q H, Yao J C. System of generalized variational inequalities and their applications[J].Appl Anal,2000,76(3/4): 203—217. doi: 10.1080/00036810008840877
[8]	Ansari Q H, Schaible S, Yao J C. System of vector equilibrium problems and their applications[J].J Optim Theory Appl,2000,107(3):547—557. doi: 10.1023/A:1026495115191
[9]	Ding X P,Park J Y. Fixed points and generalized vector equilibrium problems in G-convex spaces[J].Indian J Pure Appl Math,2003,34(6):973—990.
[10]	DING Xie-ping,Park J Y. Generalized vector equilibrium problems in generalized convex space[J].J Optim Theory Appl,2004,120(2)：327—353. doi: 10.1023/B:JOTA.0000015687.95813.a0
[11]	Ansari Q H, Yao J C. An existence result for the generalized vector equilibrium problem[J].Appl Math Lett,1999,12(8):53—56.
[12]	Oettli W,SchlAa¨ger D. Existence of equilibria for g-monotone mappings[A].In:W Takahashi，T Tanaka Eds.Nonlinear Analysis and Convex Analysis[C].Singapore:World Scientific Pub,1999,26—33.
[13]	Lin L J, Yu Z T. Fixed-point theorems and equilibrium problems[J].Nonlinear Anal,2001,43:987—999. doi: 10.1016/S0362-546X(99)00202-3
[14]	丁协平.乘积G-凸空间内的GB-优化映象的极大元及其应用(Ⅰ)[J].应用数学和力学，2003，24(6)：583—594.
[15]	丁协平.乘积G-凸空间内的GB-优化映象的极大元及其应用(Ⅱ)[J].应用数学和力学，2003，24(9)：899—905.
[16]	Park S, Kim H. Coincidence theorems for admissible multifunctions on generalized convex spaces[J].J Math Anal Appl,1996,197(1):173—187. doi: 10.1006/jmaa.1996.0014
[17]	Park S, Kim H. Foundations of the KKM theory on generalized convex spaces[J].J Math Anal Appl,1997,209(3):551—571. doi: 10.1006/jmaa.1997.5388
[18]	Park S. Continuous selection theorems for admissible multifunctions on generalized convex spaces[J].Numer Funct Anal Optimiz,1999,25(3):567—583.
[19]	Park S. Fixed points of admissible maps on generalized convex spaces[J].J Korean Math Soc,2000,37(4):885—899.
[20]	Tan K K, Zhang X L. Fixed point theorems on G-convex spaces and applications[J].Proc Nonlinear Funct Anal Appl,1996,1:1—19.
[21]	Deguire P, Tan K K, Yuan X Z. The study of maximal elements,fixed points for LS-majorized mappings and their applications to minimax and variational inequalities in product topological spaces[J].Nonlinear Anal,1999,37:933—951. doi: 10.1016/S0362-546X(98)00084-4
[22]	Park S,Kim H, Coincidence theorems on a product of generalized convex spaces and applications to equilibria[J].J Korean Math Soc,1999, 36(4):813—828.
[23]	Aubin J P, Ekeland I. Applied Nonlinear Analysis[M].New York:John Wiley & Sons,1984.