Journal of Convex Analysis 32 (2025), No. 1, 071--089
Copyright Heldermann Verlag 2025
Quasi-Equilibrium Problems with Non-Self Constraint Maps in Topological Spaces. Necessary and Sufficient Conditions for the Existence of Solutions
Didier Aussel
Lab. PROMES, UPR CNRS 8521, Université de Perpignan, France
aussel@univ-perp.fr
John Cotrina
Universidad del Pacífico, Lima, Peru
cotrina_je@up.edu.pe
Quasi-equilibrium problems represent a general framework covering, in many situations, quasi-variational inequalities, complementarity problems and generalized Nash equilibrium problems. In this work, we provide necessary and sufficient conditions guaranteeing the existence of a new kind of solution for quasi-equilibrium problems defined on Hausdorff topological spaces with non-self constraint maps. The main machineries for proving our results are a Tian's fixed point theorem for the convex case, and the finite intersection property for the non-convex case. Furthermore, quasi-variational inequality problems and generalized Nash equilibrium problems are considered as applications.
Keywords: Quasi-equilibrium problems, quasi-variational inequalities, generalized Nash equilibrium problems, non-self maps, finite intersection property.
MSC: 47J20, 49J53, 91A10.
[ Fulltext-pdf (147 KB)] for subscribers only.