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On vector variational inequalities in reflexive Banach spaces. (English) Zbl 1097.49009
Summary: In this paper, we study the solvability for a class of vector variational inequalities in reflexive Banach spaces. Using the Brouwer fixed point theorem, we prove the solvability for this class of vector variational inequalities without monotonicity assumption. The solvability results for this class of vector variational inequalities with monotone mappings are also presented by using the KKM-Fan lemma

MSC:
49J40 Variational inequalities
90C29 Multi-objective and goal programming
47J20 Variational and other types of inequalities involving nonlinear operators (general)
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