Existence of solutions of inverted variational inequalities (Q2859486)

The interesting paper under review deals with the existence of solutions of inverted variational inequalities. More precisely, the author introduces two new generalized variational inequalities and provides some existence results for these, involving operators which belong to a recently introduced class of \(ql\)-type operators [\textit{S. László}, J. Optim. Theory Appl. 150, No. 3, 425--443 (2011; Zbl 1228.49013)]. It is shown that, under some circumstances, the set of solutions of these variational inequalities coincide, a result which may be viewed as a generalization of the Minty theorem. As an application, the author shows that the Brouwer fixed point theorem is an easy consequence of the results of the paper.