Search

In this paper we prove the existence of solutions of regularized set-valued variational inequalities involving Brezis pseudomonotone operators in reflexive and locally uniformly convex Banach spaces. By taking advantage of this result, we approximate a general set-valued variational inequality with suitable regularized set-valued variational inequalities, and we show that their solutions weakly converge to a solution of the original one. Furthermore, by strengthening the coercivity conditions, we can prove the strong convergence of the approximate solutions.

In this paper, we provide sufficient conditions entailing the existence of weak sharp efficient points of a multiobjective optimization problem. The approach uses variational analysis techniques, like regularity and subregularity of the diagonal subdifferential map related to a suitable scalar equilibrium problem naturally associated to the multiobjective optimization problem.

In this paper we investigate the Aubin property of the solution map of a parametric equilibrium problem, by providing a connection with a suitable behaviour of the diagonal subdifferential operator associated to the equilibrium bifunction. In particular, we shed some light on the relationship between metric regularity and subregularity of the diagonal subdifferential, on one side, and some properties of the bifunction, on the other side.

This work deals with non-global inverse map results for the sum of two maps. We prove two theorems which shed some new light on this aspect. Some implications in terms of sensitivity of parametric generalized equations are investigated. Finally, a class of well-conditioned operators is identified.

We introduce a regularized equilibrium problem in Banach spaces, involving generalized Bregman functions. For this regularized problem, we establish the existence and uniqueness of solutions. These regularizations yield a proximal-like method for solving equilibrium problems in Banach spaces. We prove that the proximal sequence is an asymptotically solving sequence when the dual space is uniformly convex. Moreover, we prove that all weak accumulation points are solutions if the equilibrium function is lower semicontinuous in its first variable. We prove, under additional assumptions, that the proximal sequence converges weakly to a solution. Refereed/Peer-reviewed

The main purpose of this paper is the study of sufficient conditions for the existence of solutions of vector equilibrium problems. Our main results permit to obtain some existence results already established for the scalar case and, to provide some applications in the area of vector optimization and vector saddle point problems.

K.Thisresulthasmanyinterestingapplicationsconcerning xedpointtheorems,vari-ationalinequalities,potentialtheory,mathematicaleconomy,etc.ItisalsoknownthatKyFan’sminimaxinequalityisoneoftheseveralstatementswhichareequivalentto each other: Brouwer’s xed point theorem, the lemma of Knaster{Kuratowski{Mazurkiewicz,thetheoremofBrowderconcerningvariationalinequalities,the xedpointtheoremofKakutani,the xedpointtheoremofKyFan{Glicksberg,theNash