Generalized Vector Equilibrium Problems With Moving Cone And Vector Complementarity Problems

In this paper, we mainly discuss the existence results of generalized vector equilibrium problems. We mainly use the proerties of quasi-interior of the dual cone and the well-known Fan-Glicksberg-Kakutani fixed point theorem to get the existence results. As an application, we get the existence results of the vector complementarity problems. The paper is organized as follows. In Sec.1, we introduce the fonnulations of the generalized vector equilibrium problems and vector complementarity problems. In Sec.2, we recall some definitions and lemmas which are used in the paper. In Sec.3, by the fixed point theorem and the virtue of quasi-interior of dual cone, we derive existence theorems for (GVEP) and (VCP). In addition, these problems discussed in this paper are so general that our results extend and unify some recent existence results of some similar problems.