Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds

Abstract generalized vector quasi-equilibrium problems in noncompact Hadamard manifolds

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Abstract This paper deals with the abstract generalized vector quasi-equilibrium thd deliclin? soap 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 15-fc0093dx 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.