From quasivariational inclusion problems to Stampacchia vector quasiequilibrium problems, Stampacchia set-valued vector Ekeland’s variational principle and Caristi’s fixed point theorem

In this paper, we first study existence theorems of solution for quasivariational inclusion problems. We apply existence theorems of solution for quasivariational inclusion problem to study the existence theorems of solution for the Stampacchia generalized vector quasiequilibrium problems and Stampacchia vector quasiequilibrium problems. Our results and approach to the Stampacchia generalized vector quasiequilibrium problem are different from any existence results of this type of problem. Finally, we apply the existence theorems of solution for the Stampacchia vector quasiequilibrium problems to study simultaneous solutions of Caristi’s fixed point theorem and the Stampacchia set-valued vector Ekeland’s variational principle. Our results on Stampacchia set-valued vector Ekeland’s variational principle are different from any existence results of these types of problems.