Existence of a solution and variational principles for vector equilibrium problems

In this paper, we prove an existence result for a solution to the vector eq uilibrium problems. Then, we establish variational principles, that is, vec tor optimization formulations of set-valued maps for vector equilibrium pro blems. A perturbation function is involved in our variational principles. W e prove also that the solution sets of our vector optimization problems of set-valued maps contain or coincide with the solution sets of vector equili brium problems.