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

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## Abstract

This paper provides necessary and sufficient conditions for fixed-point theorems, minimax inequalities and some related theorems defined on arbitrary topological spaces that may be discrete, continuum, non-compact or non-convex. We establish a single condition, γ-recursive 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 |
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Original Title: | A Full Characterization on Fixed-Point Theorem, Minimax Inequality, Saddle Point, and KKM Theorem |

Language: | English |

Keywords: | Fixed-point 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.uni-muenchen.de/id/eprint/57929 |