Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifoldsReport as inadecuate




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Journal of Inequalities and Applications

, 2017:107

First Online: 10 May 2017Received: 01 February 2017Accepted: 21 April 2017DOI: 10.1186-s13660-017-1375-2

Cite this article as: Lu, H. & Wang, Z. J Inequal Appl 2017 2017: 107. doi: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.

KeywordsHadamard manifold maximal element abstract generalized vector quasi-equilibrium problem variational inequality MSC90C33 91E10 65K05 47J25 



Author: Haishu Lu - Zhihua Wang

Source: https://link.springer.com/







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