An Existence Result for Quasi-Equilibrium Problems

Recently M. Castellani and M. Giuli [J. Global Optim. 57 (2013) 1213–1227] showed that the proof of the existence result for quasimonotone Stampacchia variational inequalities developed by D. Aussel and N. Hadjisavvas [J. Optim. Theory Appl. 121 (2004) 445–450] can be adapted to the case of equilibrium problems. This proof was based on KKM techniques. In this paper we define and study the so-called quasi-equilibrium problem, that is an equilibrium problem with a constraint set depending on the current point. Our main contribution consists of an existence result combining fixed point techniques with stability analysis of perturbed equilibrium problems