Stampacchia Generalized Vector Quasi-Equilibrium Problems

In this paper, we mainly discuss the existence results of the stampacchia generalized vector quasi-equilibrium problems. The paper is organized as below. In Sec.1, we introduce the formulations of the weak generalized vector quasi-equilibrium problem and the Stampacchia generalized vector quasi-equilibrium problem. In Sec.2, we recall some definitions and lemmas which are used in the paper. In Sec.3, by virtue of the continuous partition of unity theorem and the scalarization method, we derive existence theorems in the case that the condition of continuity is somewhat weak. As an application, we obtain the existence theorem of the vector variational inequality. In Sec.4, we discuss the existence results in the case that the domain is unbounded. In Sec.5, we discuss the existence results in the case that there are some coercive conditions. In Sec.6, we discuss the existence results in the case that there are some monotone conditions. In additional, these problems discussed in this paper are so general that our results extend and unify some recent existence results of some similar problems.