Massimiliano Giuli

Refinements of existence results for relaxed quasimonotone equilibrium problems

We consider a general equilibrium problem in a normed vector space setting and we establish sufficient conditions for the existence of solutions in compact and non compact cases. Our approach is based on the concept of upper sign property for bifunctions, which turns out to be a very weak assumption for equilibrium problems. In the framework of variational inequalities, this notion coincides with the upper sign continuity for a set-valued operator introduced by Hadjisavvas. More in general, it allows to strengthen a number of existence results for the class of relaxed

Approximate solutions of quasiequilibrium problems in Banach spaces

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Closedness of the Solution Map in Quasivariational Inequalities of Ky Fan Type

-quasimonotone equilibrium problems.

A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces

We give sufficient conditions for the equivalence between two equilibrium problems. In particular we deduce that, under suitable assumptions, an equilibrium problem has an equivalent reformulation as a generalized variational inequality. Such conditions are satisfied when the equilibrium bifunction is lower semicontinuous, coercive and quasiconvex with respect to the second variable. We also show that the equivalent generalized variational inequality inherits the same generalized monotonicity properties of the original nonconvex equilibrium problem.

Local cone approximations in mathematical programming

In this note we show that a recent existence result on quasiequilibrium problems, which seems to improve deeply some well-known results, is not correct. We exhibit a counterexample and we furnish a generalization of a lemma about continuous

An existence result for quasiequilibrium problems in separable Banach spaces

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