Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds

作者：Lu, Haishu^*; Wang, Zhihua

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017, 2017(1): 107.

DOI：10.1186/s13660-017-1375-2

• Hadamard manifold
• maximal element
• abstract generalized vector
• quasi-equilibrium problem
• variational inequality

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.

• 出版日期2017-5-10
• 单位江苏大学