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Minty lemma for inverted vector variational inequalities. (English) Zbl 1358.49008

Summary: In this paper, we introduce Stampacchia-type inverted vector variational inequalities and Minty-type inverted vector variational inequalities and discuss Minty lemma for the inequalities showing the existence of solutions to them in Banach spaces. Next, we consider the equivalence of our Minty lemma with Brouwer’s fixed-point theorem as an application.

MSC:

49J40 Variational inequalities
49J53 Set-valued and variational analysis
49K35 Optimality conditions for minimax problems
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