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
aussel@univ-perp.fr
John Cotrina
Centro de Investigación, Universidad del Pacífico, Jr. Sanchez Cerro 2141 Jesús María, Lima 11, Peru
cotrina_je@up.edu.pe
Alfredo N. Iusem
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, CEP 22460-320, Brazil
iusp@impa.br
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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