on vector equilibrium problem with generalized pseudomonotonicity

In this paper, first a short history of the notion of equilibrium problem in economics and nash game theory is stated. also the relationship between equilibrium problem and important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem are given. the concept of generalized pseudomonotonicity for vector valued bifunctions is introduced and by using it some existence results for the vector equilibrium problem, in the setting of topological vector spaces, are presented. some examples in order to illustrate the main results and compare them with the corresponding published results are furnished. further, the compactness of the solution set of vector equilibrium problem is investigated.