Existence Theorems for Generalized Noncoercive Equilibrium Problems: The Quasi-Convex Case
SIAM Journal on Optimization
New existence results for equilibrium problems
Nonlinear Analysis: Theory, Methods & Applications
On the generalized monotonicity of variational inequalities
Computers & Mathematics with Applications
On certain conditions for the existence of solutions of equilibrium problems
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
A note on stability for parametric equilibrium problems
Operations Research Letters
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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 $$\mu $$-quasimonotone equilibrium problems.