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...

A vector equilibrium problem is generally defined by a bifunction which takes values in a partially ordered vector space. In particular, when this space is endowed with a componentwise ordering, the vector equilibrium problem can be decomposed into a family of equilibrium subproblems, each of them being governed by a bifunction obtained from the initial one by selecting some of its scalar compo...

Wardrop [1] introduced the famous user equilibrium principle for traffic network, which is a scalar equilibrium principle. Smith [2] investigated that a Wardrop's user equilibrium flow is equivalent to the solution of a class of variational inequalities when the travel cost function is a scalar function. Recently, many researchers have proposed equilibrium models based on multicriteria consider...

In this paper, we studied a new kind of vector equilibrium problem, we proved the existence of solutions for this kind of equilibrium problem by using the section theorem and KKM theorem these two tools,then we generalized this kind of vector equilibrium problem to a more general case. Equilibrium problems with lower and upper bounds is a open problem proposed by Isac, Sehgal and Singh in 1999....

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a so...

The purpose of this paper is to introduce a nonlinear scalarisation function for solving a class of implicit vector equilibrium problems. We prove a scalarisation lemma to show the relation between the implicit vector equilibrium problem and the nonlinear scalarisation function. Then we derive some new existence theorems for solutions of implicit vector equilibrium problems, using the scalarisa...

We study the equilibrium measure on two-dimensional sphere in presence of an external field generated by $$r+1$$ equal point charges that are symmetrically located around north pole. The support is known as droplet. droplet has a motherbody which we characterize means vector problem (VEP) for r measures complex plane. model undergoes two transitions reflected first component minimizer VEP, name...