On a New Class of Systems of Generalized Quasi-Variational Inequalities

Abstract

We introduce new types of systems of generalized quasi-variational inequalities and we prove the existence of the solutions by using results of pair equilibrium existence for free abstract economies. We consider the fuzzy models and we also introduce the random free abstract economy and the random equilibrium pair. The existence of the solutions for the systems of quasi-variational inequalities comes as consequences of the existence of equilibrium pairs for the considered free abstract economies.

Keywords:

• Best proximity pair
• Free abstract economies
• Fuzzy games
• Random equilibria
• Random variational inequalities
• System of generalized quasi-variational inequalities

Mathematics Subject Classification:

• 47H10
• 91A47
• 91A80

Acknowledgments

Part of the special issue, “Variational Analysis and Applications.”