留言板

 引用本文: 丁协平. 乘积拓扑空间内的重合点组定理及应用(Ⅰ)[J]. 应用数学和力学, 2005, 26(12): 1401-1408.
DING Xie-ping. System of Coincidence Theorems in Product Topological Spaces and Applications(Ⅰ)[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1401-1408.
 Citation: DING Xie-ping. System of Coincidence Theorems in Product Topological Spaces and Applications(Ⅰ)[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1401-1408.

乘积拓扑空间内的重合点组定理及应用(Ⅰ)

作者简介:丁协平(1938- ),男,自贡人,教授(Tel:+86-28-84780952;E-mail:dingxip@sicnu.edu.cn)
• 中图分类号: O177.92

System of Coincidence Theorems in Product Topological Spaces and Applications(Ⅰ)

• 摘要: 首先引入了无凸性结构的有限连续拓扑空间(简称FC-空间)新概念．其次在FC-空间内建立了一个新的连续选择定理．应用此定理，在很弱的假设下，对定义在非紧FC-空间的乘积空间上的两个集值映射簇证明了某些新的重合点定理．这些结果推广了最近文献中的许多已知结果．某些应用将在后继文章中给出．
•  [1] von Neumann J.ber ein konomsiches Gleichungssystem und eine Verallgemeinering des Browerschen Fixpunktsatzes[J].Ergeb Math Kolloq,1937,8(1):73—83. [2] Browder F E.Coincidence theorems, minimax theorems,and variational inequalities[J].Contemp Math,1984,26:67—80. [3] DING Xie-ping.Coincidence theorems involving composites of acyclic mappings in contractible spaces[J].Appl Math Lett,1998,11(2):85—89. [4] DING Xie-ping.Coincidence theorems in topological spaces and their applications[J].Appl Math Lett,1999,12(7):99—105. [5] DING Xie-ping.Coincidence theorems and generalized equilibrium in topological spaces[J].Indian J Pure Appl Math,1999,30(10):1053—1062. [6] DING Xie-ping.Coincidence theorems involving composites of acyclic mappings and applications[J].Acta Math Sci,1999,19(1):53—61. [7] DING Xie-ping.Coincidence theorems with applications to minimax inequalities, section theorem and best approximation in topological spaces[J].Nonlinear Studies,2000,7(2):211—225. [8] DING Xie-ping,Park J Y.Continuous selection theorem,coincidence theorem,and generalized equilibrium in L-convex spaces[J].Comput Math Appl,2002,44(1/2):95—103. [9] Deguire P, Lassonde M.Familles sélectantes[J].Topol Methods Nonlinear Anal,1995,5(2):261—296. [10] Deguire P,Tan K K,Yuan G X Z. The study of maximal elements,fixed point for LS--majorijed mappings and their applications to minimax and variational inequalities in product topological spaces[J].Nonlinear Anal,1999,37(7):933—951. [11] 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. [12] Ansari Q H,Idzik A,YAO J C.Coincidence and fixed points with applications[J]. Topol Methods Nonlinear Anal,2000,15(1):191—202. [13] Yu Z T,Lin L J.Continuous selection and fixed point theorems[J].Nonlinear Anal,2003,52(2):445—455. [14] Lin L J.System of coincidence theorems with applications[J].J Math Anal Appl,2003,285(2):408—418. [15] DING Xie-ping.Coincidence theorems for two families of set-valued mappings on product G-convex spaces[J].J Sichuan Normal Univ,2004,27(2):111—114. [16] DING Xie-ping.New H-KKM theorems and their applications to geometric property, coincidence theorems, minimax inequality and maximal elements[J]. Indian J Pure Appl Math,1995,26(1):1—19. [17] Park S.Continuous selection theorems in generalized convex spaces[J].Numer Funct Anal Optim,1999,20(5/6):567—583. [18] Horvath C D.Some results on multivalued mappings and inequalities without convexity[A].In:Lin B L,Simons S Eds.Nonlinear and Convex Analysis[C].New York:Marcel Dekker,1987,99—106. [19] Horvath C D.Contractibility and general convexity[J].J Math Anal Appl,1991,156(2):341—357. [20] Park S,Kim H.Coincidence theorems for admissible multifunctions on generalized convex spaces[J].J Math Anal Appl,1996,197(1):173—187. [21] Park S,Kim H.Foundations of the KKM theory on generalized convex spaces[J].J Math Anal Appl,1997,209(2):551—571. [22] Tan K K,Zhang X L.Fixed point theorems on G-convex spaces and applications[J].Nonlinear Funct Anal Appl,1996,1(1):1—19. [23] Tarafdar E.Fixed point theorems in H-spaces and equilibrium points of abstract economies[J].J Austral Math Soc,Ser A,1992,53(1):252—260.
计量
• 文章访问数:  2779
• HTML全文浏览量:  201
• PDF下载量:  916
• 被引次数: 0
出版历程
• 收稿日期:  2004-10-10
• 修回日期:  2005-08-17
• 刊出日期:  2005-12-15

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈