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General KKM Theorem with Applications to Minimax and Variational Inequalities |
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| Authors: | Q. H. Ansari Y. C. Lin J. C. Yao |
| Affiliation: | (1) Department of Mathematics, Aligarh Muslim University, Aligarh, India;(2) Present address: Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC;(3) Center of General Education, China Medical College, Taichang, Taiwan;(4) Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC;(5) Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC |
| 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 |
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