Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems |
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Authors: | Ya-Ping Fang Nan-Jing Huang Jen-Chih Yao |
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Affiliation: | (1) Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, People’s Republic of China;(2) Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, Republic of China |
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Abstract: | We generalize the concept of well-posedness to a mixed variational inequality and give some characterizations of its well-posedness. Under suitable conditions, we prove that the well-posedness of a mixed variational inequality is equivalent to the well-posedness of a corresponding inclusion problem. We also discuss the relations between the well- posedness of a mixed variational inequality and the well-posedness of a fixed point problem. Finally, we derive some conditions under which a mixed variational inequality is well-posed. This work was supported by the National Natural Science Foundation of China (10671135) and Specialized Research Fund for the Doctoral Program of Higher Education (20060610005). The research of the third author was partially support by NSC 95-2221-E-110-078. |
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Keywords: | Mixed variational inequality Inclusion problem Fixed point problem Well-posedness |
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