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Some generalized vector variational inequalities and complementarity problems for multivalued mappings. (English) Zbl 1041.49009

Summary: We introduce and study a new class of generalized vector variational inequalities and complementarity problems for multivalued mappings. We prove the existence of solutions for this kind of inequalities and discuss the relations between the solutions of the generalized vector variational inequalities and the solutions of generalized vector complementarity problems in Hausdorff topological vector spaces. Our results extend and improve some results in this field.

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J53 Set-valued and variational analysis
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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