A minimax theorem and two existence theorems of solutions for generalized quasi-variational inequalities in \(H\)-spaces
The authors present three minimax existence theorems for solutions of generalized quasi-variational inequalities for multivalued mappings in Hausdorff spaces. The first theorem generalizes to \(H\)-spaces the well-known Sion's general minimax theorem [\textit{M. Sion}, Pac. J. Math. 8, 171-176 (1958; Zbl 0081.11502)], at the same time weakening semicontinuity conditions. The next theorem is a generalization of Browder's fixed point theorem [\textit{F. E. Browder}, Math. Ann. 177, 283-301 (1968; Zbl 0176.45204)] while the third one enables to study quasi-variational inequalities for semicontinuous multivalued mappings with nonempty compact weak \(H\)-convex values.
scientific article; zbMATH DE number 1446783