Scalarized system of nonsmooth vector quasi-variational inequalities with applications to Debreu type vector equilibrium problems. (English) Zbl 1310.47083
Summary: In this work, we utilize a scalarization method to introduce a system of nonsmooth vector quasi-variational inequalities. We also study their relationship to Debreu type vector equilibrium problems. Then we establish some existence results for solutions of these systems by using maximal element theorems for a family of set-valued maps.
MSC:
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
Keywords:
scalarization; system of nonsmooth vector quasi-variational inequalities; system of Debreu type equilibrium problem for vector-valued functions; system of vector quasi-equilibrium problems; Clarke generalized directional derivative; maximal element theorem; \(\Phi\)-condensing mapsReferences:
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