Stability of solutions for variational relation problems with applications

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• 作者：Yong Jian Pu ; Zhe Yang ; ^{zheyang211@163.com}
• 关键词：Variational relations ; Essential point ; Essential component ; Ky Fan&rsquo ; s point ; Nash equilibrium ; KKM points ; Ky Fan&rsquo ; s section theorem
• 刊名：Nonlinear Analysis
• 出版年：2012
• 出版时间：March 2012
• 年：2012
• 卷：75
• 期：4
• 页码：1758-1767
• 全文大小：248 K

文摘

In this paper, we prove that most of problems in variational relations (in the sense of Baire category) are essential and that, for any problem in variational relations, 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¡¯s minimax inequality theorem, the existence of essential components of the set of Nash equilibrium points for general n-person non-cooperative games, the existence of essential component of the set of solutions for vector Ky Fan¡¯s minimax inequality, the existence of essential components of the set of KKM points and the existence of essential components of the set of solutions for Ky Fan¡¯s section theorem.