  A sufficient condition for the existence of a solution for generalized vector
equilibrium problem (GVEP) on Hadamard manifold, by using a version of KKM
lemma on this context, is presented in this paper. It is worth to point out
that, in particular, existence result of solution for optimization problems,
vector optimization problems, Nash equilibria problems, complementarity
problems and variational inequality problems can be obtained as a special case
of the existence result for GVEP in this new context.
