Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds

• Main Authors: Haishu Lu, Zhihua Wang
• Format: Article
• Language: English
• Published: SpringerOpen 2017-05-01
• Series: Journal of Inequalities and Applications
• Subjects: Hadamard manifold; maximal element; abstract generalized vector; quasi-equilibrium problem; variational inequality
• Online Access: http://link.springer.com/article/10.1186/s13660-017-1375-2

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 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 known results in the literature.