A Full Characterization on Fixed-Point Theorem, Minimax Inequality, Saddle Point, and KKM Theorem

Guoqiang Tian

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Fixed-point theorems; minimax inequalities; saddle points; FKKM theorems; recursive transfer continuity (search for similar items in EconPapers)
JEL-codes: D00 (search for similar items in EconPapers)
Date: 2012-11, Revised 2014-07
New Economics Papers: this item is included in nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/57929/1/MPRA_paper_57929.pdf original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:57929

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().