Abstract This paper deals with the abstract generalized vector quasi-equilibrium problem in noncompact Hadamard manifolds.We prove the existence of solutions to the abstract generalized vector quasi-equilibrium problem under suitable conditions and provide applications to an abstract vector quasi-equilibrium problem, a generalized scalar equilibrium problem, a Curtains scalar equilibrium problem, and a perturbed saddle point problem.Finally, as an application of the existence of solutions to the generalized scalar equilibrium problem, we obtain a weakly mixed variational inequality and two mixed variational inequalities.
The results presented in this paper unify and generalize many Beard Nets known results in the literature.