General KKM Theorem with Applications to Minimax and Variational Inequalities

Q. H. Ansari, Y. C. Lin and J. C. Yao
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Q. H. Ansari: Aligarh Muslim University
Y. C. Lin: China Medical College
J. C. Yao: National Sun Yat-Sen University

Journal of Optimization Theory and Applications, 2000, vol. 104, issue 1, No 2, 17-57

Abstract: Abstract In this paper, a general version of the KKM theorem is derived by using the concept of generalized KKM mappings introduced by Chang and Zhang. By employing our general KKM theorem, we obtain a general minimax inequality which contains several existing ones as special cases. As applications of our general minimax inequality, we derive an existence result for saddle-point problems under general setting. We also establish several existence results for generalized variation inequalities and generalized quasi-variational inequalities.

Keywords: generalized KKM mappings; transfer closed-valued mappings; γ-transfer lower semi-continuous functions; minimax inequalities; generalized variational inequalities; generalized quasi-variational inequalities (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (5)

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DOI: 10.1023/A:1004620620928

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