Abstract

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

Author information

Contact details are reproduced from the original publication and may be historical.

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, Perú

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

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Suggested citation

D. Aussel, J. Cotrina, A. N. Iusem. “An Existence Result for Quasi-Equilibrium Problems.” Journal of Convex Analysis 24 (2017), No. 1, 55–66. https://doi.org/10.68381/jca24004

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