H\"{o}lder continuity of solutions to parametric primal and dual vector mixed quasi-equilibrium problems

Abstract:

In this paper, following the dual rules for an equilibrium problem, we introduce the corresponding parametric dual vector mixed quasi-equilibrium problem, which is Mix Minty-type parametric dual vector quasi-equilibrium problem. We discuss the H\"{o}lder continuity of the solutions of parametric primal vector mixed quasi-equilibrium problem (PVMQEPi)(i=1,2) and parametric dual vector mixed quasi-equilibrium problem(DVMQEPi)(i=1,2) in general settings and also provide suitable remarks and examples to illustrate our results on by one. Finally, we apply Mixed Minty-type dual vector mixed quasi-equilibrium problems to deal with Mix Minty variational inequality as an application. Our results improve and extend the corresponding results announced by many others.