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Well-posedness of generalized mixed variational inequalities,inclusion problems and fixed-point problems
Institution:1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;2. Department of Applied Mathematics, National Sun Yat-sen University, 804 Kaohsiung, Taiwan
Abstract:We introduced and studied the concept of well-posedness to a generalized mixed variational inequality. Some characterizations are given. Under suitable conditions, we prove that the well-posedness of the generalized mixed variational inequality is equivalent to the well-posedness of the corresponding inclusion problem. We also discuss the relations between the well-posedness of the generalized mixed variational inequality and the well-posedness of the corresponding fixed-point problem. Finally, we derive some conditions under which the generalized mixed variational inequality is well-posed.
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