In this paper, we introduce a system of vector equilibrium problems and prove the existence of a solution. As an application, we derive some existence results for the system of vector variational inequalities. We also establish some existence results for the system of vector optimization problems, which includes the Nash equilibrium problem as a special case.

Abstract: In this work, a nonsmooth multiobjective optimization problem involving generalized invexity with cone constraints and Applications (for short, (MOP)) is considered. The Kuhn-Tucker necessary and sufficient conditions for (MOP) are established by using a generalized alternative theorem of Craven and Yang. The relationship between weakly efficient solutions of (MOP) and vector valued s...

The purpose of this paper is to introduce and study Generalized Minty Variational Inequalities in Banach spaces. We consider a problem of vector variational inequalities, referred as Generalized Minty VI(f ′ − , K), in a real Banach space X, where K is a nonempty subset of X and f ′ − is the lower Dini directional derivative of a real function f defined on an open set in X containing K. The res...

<p style='text-indent:20px;'>This paper deals with the weak versions of vector variational-like inequalities, namely Stampacchia and Minty type under invexity in framework convexificators. The connection between both problems along link to optimization problem are analyzed. An application nonconvex mathematical programming has also been presented. Further, bi-level version these is formul...

In this paper we introduce notions of well-posedness for a vector optimization problem and for a vector variational inequality of differential type, we study their basic properties and we establish the links among them. The proposed concept of well-posedness for a vector optimization problem generalizes the notion of well-setness for scalar optimization problems, introduced in [2]. On the other...

We present the solvability of a class of nonlinear variational inequalities involving pseudomonotone operators in a locally convex Hausdorff topologi-cal vector spaces setting. The obtained result generalizes similar variation-al inequality problems on monotone operators.