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Bifunction hemivariational inequalities. (English) Zbl 1211.49013
Summary: We introduce and consider a new class of variational inequalities, which is called the bifunction hemivariational inequality. This new class includes several classes of variational inequalities as special cases. A number of iterative methods for solving bifunction hemivariational inequalities are suggested and analyzed by using the auxiliary principle technique. We also study the convergence analysis of these iterative methods under some mild conditions. The results obtained in this paper can be considered as a novel application of the auxiliary principle technique.

MSC:
49J40 Variational inequalities
49M30 Other numerical methods in calculus of variations (MSC2010)
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