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A unified approach for a class of problems involving a pseudo-monotone operator. (English) Zbl 1157.47046

In this paper, the authors consider a variational inequality problem over the union of a set and a sequence of sets, and also over only the union of sets. They obtain an abstract existence result for a solution of such a variational inequality problem and the established a Hartman-Stampacchia type result for the solutions. The study is motivated by the unifying effect of such a result and its large applicability. The authors use their abstract result to prove various existence and approximation results for a class of variational-hemivariational inequalities involving pseudo-monotone operators. Their approach mainly relies on Galerkin like approximations, pseudo-monotone operators and topics from nonsmooth analysis.

MSC:

47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J40 Variational inequalities
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
49J52 Nonsmooth analysis
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