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Ceng, L. C.; Yao, J. C.

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

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 12, 4585-4603 (2008).
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.

Cited in 29 Documents

MSC:

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

Keywords:

generalized mixed variational inequalities; inclusion problem; fixed-point problem; well-posedness; KKM-fan Lemma; Hausdorff metric; Nadler’s result
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\textit{L. C. Ceng} and \textit{J. C. Yao}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 12, 4585--4603 (2008; Zbl 1153.49024)
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