局部G-凸空间内的广义矢量拟平衡问题

丁协平

局部G-凸空间内的广义矢量拟平衡问题

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: 四川省教育厅重点科研基金资助项目(2003A081;SZD0406)

详细信息

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

中图分类号: O255；O177.92
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- 文章访问数: 2210
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- 被引次数: 0
出版历程
- 收稿日期: 2003-06-30
- 修回日期: 2005-01-18
- 刊出日期: 2005-05-15

Generalized Vector Quasi-Equilibrium Problems in Locally G-Convex Spaces

DING Xie-ping

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

摘要

摘要: 在局部G-凸空间内引入和研究了几类广义矢量拟平衡问题(GVQEP)．包含了大多数广义矢量平衡问题，广义矢量变分不等式问题，拟平衡问题和拟变分不等式问题作为特殊情形．首先在局部G-凸空间内对一人对策证明了一个平衡存在性定理．作为应用，在非紧局部G-凸空间内对GVQEP的解建立了某些新的存在定理．这些结果和论证方法与最近文献中的结果和论证方法相比较是新的和完全不同的．
- 广义矢量拟平衡问题 /
- 一人对策 /
- 平衡 /
- 局部G-凸空间
Abstract: Some classes of generalized vector quasi-equilibrium problems (in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems, generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.
- generalized vector quasi-equilibrium problem /
- one person game /
- equilibrium /
- locally G-convex space

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参考文献(24)

[1]	LIN Lai-jiu,YU Zenn-tseun.On some equilibrium problems for Multimaps[J].J Comput Appl Math, 2001,129(1/2):171—183. doi: 10.1016/S0377-0427(00)00548-3
[2]	DING Xie-ping.Quasi-variational inequalities and social equilibrium[J].Appl Math Mech，1991,12(7):639—646. doi: 10.1007/BF02018945
[3]	DING Xie-ping.Existence of solutions for quasi-equilibrium problems[J].J Sichuan Normal Univ,1998,21(6):603—608.
[4]	DING Xie-ping.Existence of solutions for quasi-equilibrium problems in noncompact topological spaces[J].Computers Math Appl,2000,39(3/4):13—21.
[5]	DING Xie-ping. Quasi-equilibrium problems with applications to infinite optimization and constrained games in noncompact topological spaces[J].Appl Math Lett,2000,13(3):21—26.
[6]	DING Xie-ping. Quasi-equilibrium problems and constrained multiobjective games in generalized convex spaces[J]. Appl Math Mech,2001,22(2):160—172.
[7]	DING Xie-ping. Maximal element principles on generalized convex spaces and their applications[A].In:Argawal R P Ed.Mathematical Analysis and Applications (4)[C]. London: Taylor & Francis, 2002,149—174.
[8]	LIN Lai-jiu, Park S. On some generalized quasi-equilibrium problems[J].J Math Anal Appl, 1998,224(2): 167—181. doi: 10.1006/jmaa.1998.5964
[9]	CHEN Ming-po, LIN Lai-jiu, Park S. Remarks on generalized quasi-equilibrium problems[J].Nonlinear Anal, 2003,52(2):433—444. doi: 10.1016/S0362-546X(02)00106-2
[10]	Park S. Fixed points and quasi-equilibrium problems[J].Math Computer Modelling,2000,32(11/13):1297—1304. doi: 10.1016/S0895-7177(00)00204-1
[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, Schlager D. Existence of equilibria for g-monotone mappings[A].In:Takahashi W,Tanaka T Eds.Nonlinear Analysis and Convex Analysis[C].Singapore:World Scientific Pub, 1999,26—33.
[13]	DING Xie-ping,Park J Y. Fixed points and generalized vector equilibria in G-convex spaces[J]. Indian J Pure Appl Math,2003,34(6):973—990.
[14]	DING Xie-ping, Park J Y. Generalized vector equilibrium problems in generalized convex spaces[J]. J Optim Theory Appl,2004,120(2):225—235.
[15]	LIN Lai-jiu, YU Zenn-tsuen, Kassay G. Existence of equilibria for multivalued mappings and its application to vectorial equilibria[J].J Optim Theory Appl, 2002,114(1):189—208. doi: 10.1023/A:1015420322818
[16]	Giannessi F.Vector Variational Inequalities and Vector Equilibria[M].London: Kluwer Academic Publishers, 2000,403—422.
[17]	Park S. Fixed points of better admissible maps on generalized convex spaces[J].J Korean Math Soc, 2000,37(6)：885—899.
[18]	Park S. Fixed point theorems in locally G-convex spaces[J].Nonlinear Anal, 2002,48(6): 869—875. doi: 10.1016/S0362-546X(00)00220-0
[19]	Park S, Kim H. Foundations of the KKM theory on generalized convex spaces[J].J Math Anal Appl,1997,209(2): 551—571. doi: 10.1006/jmaa.1997.5388
[20]	Tarafdar E. Fixed point theorems in locally H-convex uniform spaces[J]. Nonlinear Anal,1997,29(9):971—978. doi: 10.1016/S0362-546X(96)00174-5
[21]	Horvath C D. Contractibility and generalized convexity[J].J Math Anal Appl, 1991,156(2):341—357. doi: 10.1016/0022-247X(91)90402-L
[22]	Aliprantis C D, Border K C.Infinite Dimensional Analysis[M].New York: Springer-Verlag, 1994,456—520.
[23]	YUAN Xian-zhi.KKM Theory and Applications in Nonlinear Analysis[M].New York: Marcel Dekker, Inc,1999，229—321.
[24]	Aubin J P, Ekeland I.Applied Nonlinear Analysis[M].New York:John Wiley & Sons, 1984.