In this paper we study the solvability of the generalized vector equilibrium problem (for short, GVEP) with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVEPs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVEPs without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also the extension and improvement of some recent results in the literature.
