Remarks on generalized quasi-equilibrium problems Original Research Article

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 Himmelbergʹs 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.