FC-空间中的KKM型定理与截口定理  

KKM Type Theorem and Section Theorem in FC-Spaces

作　　者：王彬[1] 

机构地区：[1]内江师范学院数学系,四川内江641112

出　　处：《重庆师范大学学报（自然科学版）》2008年第2期25-28,36,共5页Journal of Chongqing Normal University:Natural Science

基　　金：四川省教育厅重点科研基金(No.2003A081);四川省教育厅重点学科基金(No.SZD0406)

摘　　要：在没有任何凸性结构和线性结构的有限连续空间中引入了FC-KKM映象的概念,并在FC-空间中证明了一个新的非空交定理,利用该非空交定理证明了一个新的不动点定理,再利用该不动点定理以及B rouwer不动点定理和连续单位分解定理在FC-空间中证明了一个具有FC-KKM映象的FC-KKM定理和FC-空间截口定理,并将所得结果应用于重合点问题的研究,证明了一个FC-空间中新的重合点定理,推广了近期的相关文献。In 1929, Knaster, Kuratowski and Mazurkiewicz established the celebrated KKM theorem and its generalizations are of fundamental importance in modern nonlinear analysis. Recently many authors have also extended KKM mapping and established corresponding KKM theorems,section theorems,fixed point theorems and coincidence theorems in several kinds of spaces. In this paper the concept of FC-KKM mapping is introduced in finitely continuous topological spaces without any convexity and linear structure. Meanwhile, a new nonempty intersection theorem is proved in finitely continuous topological spaces without any convexity and linear structure. By applying the nonempty intersection theorem , we prove a new fixed point theorem with transfer closed valued mapping in finitely continuous topological spaces without any convexity and linear Structure. And a new FC-KKM type theorems with transfer closed valued mapping and section theorems are proved in finitely continuous topological spaces without any convexity and linear structure by applying the fixed point theorem, Brouwer fixed point theorem and the continuous partition of unity theorem . In application,we utilize those resuits to study the coincidence point problem and prove a new coincidence theorem with transfer open valued mapping in finitely continuous topological spaces without any convexity and linear structure. These results extend and generalize some known results.

关 键 词：FC-空间 转移开(闭)映象 FC-KKM映象 截口定理 重合定理 

分 类 号：O189.25[理学—数学]