Generalized variational inequalities of the Hartman–Stampacchia–Browder type

Abstract

We obtain several generalized variational inequalities from an equilibrium theorem due to the first author under more weaker hypothesis and in more general setting than known ones. Our new results extend, unify and improve many known Hartman–Stampacchia–Browder type variational inequalities for u.s.c. or monotone type multimaps. Our proofs are also much simpler than known ones.

Keywords

• σ(F,E)-topology
• δ((F,E))-topology
• η((F,E))-topology
• Convex space
• Variational inequalities
• Demimonotone multimap