Tykhonov well-posedness for lexicographic equilibrium problems |
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| Authors: | Lam Quoc Anh Tran Quoc Duy |
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| Institution: | 1. Department of Mathematics, Teacher College, Cantho University, Cantho, Vietnam.quocanh@ctu.edu.vn;3. Department of Mathematics, University of Science, Vietnam National University, Hochiminh City, Vietnam.;4. Department of Mathematics, Cantho Technical Economic College, Cantho, Vietnam. |
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| Abstract: | In this paper, we consider the vector equilibrium problems involving lexicographic cone in Banach spaces. We introduce the new concepts of the Tykhonov well-posedness for such problems. The corresponding concepts of the Tykhonov well-posedness in the generalized sense are also proposed and studied. Some metric characterizations of well-posedness for such problems are given. As an application of the main results, several results on well-posedness for the class of lexicographic variational inequalities are derived. |
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| Keywords: | Lexicographic order equilibrium problems variational inequalities Tykhonov well-posedness |
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