KKM Type Theorem and Section Theorem in FCSpaces
WANG Bin(Dept.of Mathematics,Neijiang Teachers College,Neijiang Sichuan 641112,China)
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 FCKKM 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 FCKKM 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 results 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.


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WANG Bin1,2, SHI Yongguo1(1. College of Mathematics and Information Science,Neijiang Normal University,Neijiang 641112,Sichuan;2. Key Laboratory of Numerical Simulation of Sichuan Province,Neijiang Normal University,Neijiang 641112,Sichuan);Section Theorem and Its Applications in FCSpaces[J];Journal of Sichuan Normal University(Natural Science);200905 



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