## Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems.(English)Zbl 1149.49009

Summary: 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.

### MSC:

 49J40 Variational inequalities 49K40 Sensitivity, stability, well-posedness 90C31 Sensitivity, stability, parametric optimization 47H10 Fixed-point theorems
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### References:

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