Tian, Guoqiang (2012): A Full Characterization on FixedPoint Theorem, Minimax Inequality, Saddle Point, and KKM Theorem.

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Abstract
This paper provides necessary and sufficient conditions for fixedpoint theorems, minimax inequalities and some related theorems defined on arbitrary topological spaces that may be discrete, continuum, noncompact or nonconvex. We establish a single condition, γrecursive transfer lower semicontinuity, which fully characterizes the existence of equilibrium of minimax inequality without imposing any kind of convexity nor any restriction on topological space. The result then is employed to fully characterize fixed point theory, saddle point theory, and the FKKM theory.
Item Type:  MPRA Paper 

Original Title:  A Full Characterization on FixedPoint Theorem, Minimax Inequality, Saddle Point, and KKM Theorem 
Language:  English 
Keywords:  Fixedpoint theorems, minimax inequalities, saddle points, FKKM theorems, recursive transfer continuity 
Subjects:  D  Microeconomics > D0  General > D00  General 
Item ID:  57929 
Depositing User:  Guoqiang Tian 
Date Deposited:  14 Aug 2014 12:06 
Last Modified:  01 Oct 2019 20:53 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/57929 