局部FC-一致空间内的广义矢量拟变分包含组和广义矢量拟优化问题组

丁协平

局部FC-一致空间内的广义矢量拟变分包含组和广义矢量拟优化问题组

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: 四川省教育厅重点科研基金资助项目(07ZA092SZD0406)

详细信息

作者简介:
丁协平(1938- ),男,四川自贡人,教授(Tel:+86-28-84780952;E-mail:xieping_ding@hotmail.com).

中图分类号: O176.3；O177.92
计量
- 文章访问数: 2933
- HTML全文浏览量: 150
- PDF下载量: 719
- 被引次数: 0
出版历程
- 收稿日期: 2008-09-24
- 修回日期: 2009-01-21
- 刊出日期: 2009-03-15

Systems of Generalized Vector Quasi-Variational Inclusions and Systems of Generalized Vector Quasi-Optimization Problems in Locally FC-Uniform Spaces

DING Xie-ping

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

摘要

摘要: 在没有凸性结构的局部FC-一致空间内，引入和研究了某些新的广义矢量拟变分包含问题组和广义矢量理想(真,帕雷多(Pareto),弱)拟优化问题组．应用KKM型定理和Himmelberg型不动点定理,首先对广义矢量拟变分包含问题组的解，证明了某些新的存在性定理．作为应用,对广义矢量理想(真,帕雷多,弱)拟优化问题组的解也得到了某些新的存在性结果．
- KKM型定理 /
- Himmelberg型不动点定理 /
- 广义矢量拟变分包含问题组 /
- 广义矢量拟优化问题组 /
- 局部FC-一致空间
Abstract: Some new systems of generalized vector quasivariational inclusion problems and system of generalized vector ideal(resp., proper, Pareto, weak) quasioptimization problems in locally FC-uniform spaces without convexity structure are introduced and studied. By using KKM type theorem and Himmelberg type fixed point theorem, some new existence theorems of solutions for the systems of generalized vector quasivariational inclusion problems were first proved. As applications, some new existence results of solutions for systems of generalized vector quasioptimization problems were obtained also.
- KKM type theorem /
- Himmelberg type fixed point theorem /
- generalized vector quasivariational inclusions /
- system of generalized vector optimization problems /
- locally FC-uniform space

HTML全文

参考文献(28)

[1]	Lin L J, Tan N X. On quasivariational inclusions of type I and related problems[J].J Glob Optim,2007,39(3):393-407. doi: 10.1007/s10898-007-9143-3
[2]	Hai N X, Khanh P Q. Existence of solutions to general quasiequilibrium problems and applications[J].J Optim Theory Appl,2007,133(3):317-327. doi: 10.1007/s10957-007-9170-8
[3]	Hai N X, Khanh P Q. The solution existence of general variational inclusion problems[J].J Math Anal Appl,2007,328(2):1268-1277. doi: 10.1016/j.jmaa.2006.06.058
[4]	Hai N X, Khanh P Q. Systems of set-valued quasivariational inclusion problems[J].J Optim Theory Appl,2007,135(1):55-67. doi: 10.1007/s10957-007-9222-0
[5]	Lin L J, Shie H J. Existence theorems of quasivariational inclusion problems with applications to bilevel problems and mathem atical programs with equilibrium constraint[J].J Optim Theory Appl,2008,138(3):445-457. doi: 10.1007/s10957-008-9385-3
[6]	Lin L J.Systems of generalized quasivariational inclusion problems with applications to variational analysis and optimization problems[J].J Glob Optim,2007,38(1):21-39. doi: 10.1007/s10898-006-9081-5
[7]	Lin L J, Wang S Y, Chuang C S. Existence theorems of systems of variational inclusion problems with applications[J].J Glob Optim,2008,40(4):751-764. doi: 10.1007/s10898-007-9160-2
[8]	丁协平，黎进三，姚任之.局部FC-一致空间内的广义约束多目标对策[J].应用数学和力学，2008,29(3):272-280.
[9]	DING Xie-ping, Liou Y C, Yao J C. Generalized R-KKM type theorems in topological spaces with applications[J].Appl Math Lett,2005,18(12):1345-1350. doi: 10.1016/j.aml.2005.02.022
[10]	DING Xie-ping. Generalized game and system of generalized vector quasi-equilibrium problems in locally FC-uniform spaces[J].Nonlinear Anal,2008,68(4):1028-1036. doi: 10.1016/j.na.2006.12.003
[11]	Luc D T.Theory of Vector Optimization[M].Lectures Notes in Economics and Mathematical Systems.319.Berlin, Germany:Springer Verlag,1989.
[12]	Ben-El-Mechaiekh H, Chebbi S, Flornzano M, et al. Abstract convexity and fixed points[J].J Math Anal Appl,1998,222(1):138-150. doi: 10.1006/jmaa.1998.5918
[13]	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
[14]	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
[15]	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
[16]	丁协平.局部FC-一致空间内凝聚映象的极大元和广义对策及应用（Ⅰ）[J].应用数学和力学，2007, 28(12):1392-1399.
[17]	DING Xie-ping. Minimax inequalities and fixed points of expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces[J].Nonlinear Anal.DOI: 10.1016/j.na.2008.01.018.
[18]	Kelly J L.General Topology[M].Princeton N J:Van Nostrand,1955.
[19]	Kthe G.Topological Vector Spaces Ⅰ[M].Berlin, New York:Springer-Verlag, 1983.
[20]	丁协平.局部FC-一致空间内凝聚映象的极大元和广义对策及应用（Ⅱ）[J].应用数学和力学，2007,28(12):1400-1410.
[21]	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
[22]	Park S. Fixed point theorems in locally G-convex spaces[J].Nonlinear Anal,2002,48(6):869-879. doi: 10.1016/S0362-546X(00)00220-0
[23]	DING Xie-ping. generalizations of Himmelberg type fixed point theorems in locally FC-spaces[J].J Sichuan Normal Univ(NS),2006,29(1):1-6.
[24]	DING Xie-ping. System of generalized vector quasi-equilibrium problems in locally FC-spaces[J].Acta Math Sinica,2006,22(5):1529-1538. doi: 10.1007/s10114-005-0671-9
[25]	DING Xie-ping. Weak Pareto equilibria for generalized constrained multiobjective games in locally FC-spaces[J].Nonlinear Anal,2006,65(3):538-545. doi: 10.1016/j.na.2005.09.029
[26]	Aubin J P, Ekeland I.Applied Nonlinear Analysis[M].New York:Wiley,1984.
[27]	Aliprantis C D, Border K C.Infinite Dimensional Analysis[M].New York:Springer-Verlag,1994.
[28]	Fan K. Fixed-points and minimax theorems in locally convex topological linear spaces[J].Proc Nat Acad Sci USA,1952,38(1):131-136.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 2933
HTML全文浏览量: 150
PDF下载量: 719
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

局部FC-一致空间内的广义矢量拟变分包含组和广义矢量拟优化问题组

作者简介:
丁协平(1938- ),男,四川自贡人,教授(Tel:+86-28-84780952;E-mail:xieping_ding@hotmail.com).

计量

Systems of Generalized Vector Quasi-Variational Inclusions and Systems of Generalized Vector Quasi-Optimization Problems in Locally FC-Uniform Spaces

计量

目录

留言板

局部FC-一致空间内的广义矢量拟变分包含组和广义矢量拟优化问题组

作者简介: 丁协平(1938- ),男,四川自贡人,教授(Tel:+86-28-84780952;E-mail:xieping_ding@hotmail.com).

计量

出版历程

Systems of Generalized Vector Quasi-Variational Inclusions and Systems of Generalized Vector Quasi-Optimization Problems in Locally FC-Uniform Spaces

计量

出版历程

目录

作者简介:
丁协平(1938- ),男,四川自贡人,教授(Tel:+86-28-84780952;E-mail:xieping_ding@hotmail.com).