Essential Stability of Solutions for Maximal Element Theorem with Applications

Zaifu Yang and Y. J. Pu
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Y. J. Pu: Chong Qing University

Journal of Optimization Theory and Applications, 2011, vol. 150, issue 2, No 5, 284-297

Abstract: Abstract In this paper, we prove that most of problems in maximal element theorem (in the sense of Baire category) are essential and that, for any problem in maximal element theorem, there exists at least one essential component of its solution set. As applications, we deduce the existence of essential components of the set of Ky Fan’s points based on Ky Fan Minimax Inequality, the existence of essential components of the set of Nash equilibrium points for general n-person non-cooperative games and the existence of essential components of the set of solutions of vector Ky Fan Minimax Inequality.

Keywords: Maximal element theorem; Essential set; Essential component; Ky Fan’s points; Nash equilibrium; Vector Ky Fan Minimax Inequality (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-011-9812-8

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