## 留言板

 引用本文: 丁协平. 乘积FC-空间内涉及一较好容许集值映象的优化映象族的极大元及其应用[J]. 应用数学和力学, 2006, 27(12): 1405-1416.
DING Xie-ping. Maximal Elements of a Family of Majorized MappingsInvolving a Better Admissible Mapping in Product FC-Spaces and Applications[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1405-1416.
 Citation: DING Xie-ping. Maximal Elements of a Family of Majorized MappingsInvolving a Better Admissible Mapping in Product FC-Spaces and Applications[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1405-1416.

## 乘积FC-空间内涉及一较好容许集值映象的优化映象族的极大元及其应用

###### 作者简介:丁协平(1938- ),男,自贡人,教授(Tel:+86-28-84780952;E-mail:xieping_ding@hotmail.com).
• 中图分类号: O177.91

## Maximal Elements of a Family of Majorized MappingsInvolving a Better Admissible Mapping in Product FC-Spaces and Applications

• 摘要: 引入了涉及一较好容许集值映象的映一拓扑空间到一有限连续拓扑空间(简称,FC-空间)的优化映象族．在乘积FC-空间的非紧设置下对这类优化映象族证明了某些极大元存在性定理．在乘积FC-空间内给出了对不动点和极小极大不等式组的应用．这些定理改进、统一和推广了最近文献中的很多重要结果．
•  [1] DING Xie-ping.Maximal element theorems in product FC-spaces and generalized games[J].J Math Anal Appl,2005,305(1):29—42. [2] Lassonde M. On the use of KKM multifunctions in fixed point theory and related topics[J].J Math Anal Appl,1983,97(1):151—201. [3] Horvath C D.Contractibility and general convexity[J].J Math Anal Appl,1991,156(2):341—357. [4] Park S, Kim H.Foundations of the KKM theory on generalized convex spaces[J].J Math Anal Appl,1997,209(3):551—571. [5] Ben-El-Mechaiekh H,Chebbi S,Florenzano M,et al.Abstract convexity and fixed points[J].J Math Anal Appl,1998,222(1):138—151. [6] DING Xie-ping.Maximal element principles on generalized convex spaces and their application[A].In:Argawal R P,Ed.Set Valued Mappings With Applications in Nonlinear Analysis[C].in:SIMMA,Vol 4,2002,149—174. [7] 丁协平.乘积G-凸空间内的GB[KG*9]. -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. [8] 丁协平.乘积G-凸空间内的GB[KG*9]. -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. [9] 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(7):933—951. [10] Shen Z F.Maximal element theorems of H-majorized correspondence and existence of equilibrium for abstract economies[J].J Math Anal Appl,2001,256(1):67—79. [11] Dugundji J.Topology[M].Boston:Allyn and Bacon,1966. [12] Aubin J P,Ekeland I.Applied Nonlinear Analysis[M].New York:John Wiley & Sons,1984. [13] Yannelis N C,Prabhakar N D.Existence of maximal elements and equilibria in linear topological spaces[J].J Math Econom,1983,12(3):233—245. [14] DING Xie-ping, Tan K K.On equilibria of noncompact generalized games[J].J Math Anal Appl,1993,177(1):226—238. [15] DING Xieping,Kim W K,Tan K K.Equilibria of generalized games with L-majorized correspondences[J].Internat J Math Math Sci,1994,17(4):783—790. [16] Tulcea C I. On the equilibriums of generalized games[R]. The Center for Math Studies in Economics and Management Science, paper No 696,1986. [17] Toussaint S. On the existence of equilibria in economies with infinite commodities and without ordered preferences[J].J Econom Theory,1984,33(1):98—115. [18] Borglin A,Keiding H.Existence of equilibrium actions and of equilibrium: A note on the “new” existence theorems[J].J Math Econom,1976,3(3):313—316. [19] DING Xie-ping.Fixed points, minimax inequalities and equilibria of noncompact generalized games[J].Taiwanese J Math,1998,2(1):25—55.[JP3]. DING Xie-ping,Yuan G X -Z.The study of existence of equilibria for generalized games without lower semicontinuity in locally convex topological vector spaces[J]. J Math Anal Appl,1998,227(2):420—438.
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##### 出版历程
• 收稿日期:  2005-04-16
• 修回日期:  2006-08-10
• 刊出日期:  2006-12-15

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