Our main aim in this paper is to obtain fundamental existence theorems of quasi-equilibrium
problems and generalized quasi-equilibrium problems of multivalued functions. We use a continuous
selection theorem to show that the existence theorems of generalized quasi-equilibrium
problems are simple consequences of the corresponding quasi-equilibrium problems. We use a
generalization of Himmelberg’s theorem due to the third author for not necessary locally convex
topological vector spaces to prove the existence theorems of quasi-equilibrium problems for
multivalued functions.