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.