In this paper, we consider the system of vector quasi-equilibrium problems with or without involving -condensing maps and prove the existence of its solution. Consequently, we get existence results for a solution to the system of vector quasi-variational-like inequalities. We also prove the equivalence between the system of vector quasi-variational-like inequalities and the Debreu type equilibr...

We define the quasi-minimal elements of a set with respect to a convex cone and characterize them via linear scalarization. Then we attach to a general vector optimization problem a dual vector optimization problem with respect to quasi-efficient solutions and establish new duality results. By considering particular cases of the primal vector optimization problem we derive vector dual problems ...

In this paper, we introduce and study a class of generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. By virtue of the properties of Γ-convex and KC-map, we give some sufficient conditions to guarantee the existence of solutions for the generalized symmetric vector quasi-equilibrium problems in abstract convex spaces. As application, we show an existence theorem of...

We introduce a new system of generalized vector quasiequilibrium problems which includes system of vector quasiequilibrium problems, system of vector equilibrium problems, and vector equilibrium problems, and so forth in literature as special cases.We prove the existence of solutions for this system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results...

It is known that vector variational inequality models arises from vector optimization and vector traac equilibria. In this paper, existence results of a solution for a generalized pre-vector variational inequality and a generalized pre-quasi-vector variational inequality are established. The main condition used is that the underlying vector-valued function is assumed to be cone-quasi-convex. Th...

A spacetime is a four-manifold with a pseudo-metric of signature (+,+,+,−). A hypersurface or a 2-surface in a spacetime is spacelike if the induced metric is positive definite. A quasi-local energy-momentum vector is a vector in R associated to a spacelike 2-surface which depends on its first and second fundamental forms and the connection to its normal bundle in the spacetime. The time compon...

In this paper, we introduce four new types of the system of generalized vector quasi-equilibrium problems, and establish some new existence results of a solution for the system of vector quasi-equilibrium problems. Mathematics Subject Classification: 90C29, 49J40