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Journal of Convex Analysis 24 (2017), No. 1, 055--066
Copyright Heldermann Verlag 2017

An Existence Result for Quasi-Equilibrium Problems

Didier Aussel
Laboratoire PROMES, Université de Perpignan, Tecnosud, Rambla de la Thermodynamique, 66100 Perpignan, France

John Cotrina
Centro de Investigación, Universidad del Pacífico, Jr. Sanchez Cerro 2141 Jesús María, Lima 11, Peru

Alfredo N. Iusem
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, CEP 22460-320, Brazil

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.

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