Tian, Guoqiang (1994): Generalized KKM theorem, minimax inequalities and their applications. Published in: Journal of Optimization Theory and Applications , Vol. 83, No. 2 (November 1994): pp. 375389.

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Abstract
This paper extends the wellknown KKM theorem and variational inequalities by relaxing the closedness of values of a correspondence and lower semicontinuity of a function. The approach adopted is based on Michael's continuous selection theorem. As applications, we provide theorems for the existence of maximum elements of a binary relation, a price equilibrium, and the complementarity problem. Thus our theorems, which do not require the openness of lower sections of the preference correspondences and the lower semicontinuity of the excess demand functions, generalize many of the existence theorems such as those in Sonnenschein (Ref. 1), Yannelis and Prabhakar (Ref. 2), and Border (Ref. 3).
Item Type:  MPRA Paper 

Original Title:  Generalized KKM theorem, minimax inequalities and their applications 
Language:  English 
Keywords:  KKM theorem; Variational inequalities; Complementarity problem; Price equilibrium; Maximal elements ; Binary relations 
Subjects:  D  Microeconomics > D6  Welfare Economics > D63  Equity, Justice, Inequality, and Other Normative Criteria and Measurement 
Item ID:  41217 
Depositing User:  Guoqiang Tian 
Date Deposited:  13. Sep 2012 18:43 
Last Modified:  18. Feb 2013 02:08 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/41217 