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Well-posedness of generalized mixed variational inequalities, inclusion problems and fixed-point problems. (English) Zbl 1153.49024

Summary: We introduce and study 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.

MSC:

49K40 Sensitivity, stability, well-posedness
49J40 Variational inequalities
47H10 Fixed-point theorems
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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