Existence of solutions for generalized vector equilibrium problems

In this paper, several definitions for generalized convexity and generalized monotonicity are introduced, and the relationships between a generalized vector equilibrium problem and its dual problem for these generalized convex and generalized monotone mappings are considered. By making use of Nadler's Lemma and the fixed point theorem of set-valued mapping, the existence theorems of solutions for the generalized vector equilibrium problems are obtained. The results presented here are more general and interesting.