Vector Equilibrium Problems Research Articles

Generalized vector quasi-equilibrium problems

The properly quasi-convexity of multivalued mappings in an ordered vector space is introduced. Existence theorems for generalized vector quasi-equilibrium problems and multivalued vector equilibrium problems are obtained.

On vector equilibrium problem

This paper presents some existence results of a vector equilibrium problem. The several important special cases of the vector equilibrium problem are also discussed.

On Generalized Vector Equilibrium Problems

In this paper we prove the existence of solutions of the generalized vector equilibrium problem in the setting of Hausdorff topological vector spaces. As applications, we present some relevant particular cases: a generalized vector variational-like inequality in Hausdorff topological vector spaces, and equilibrium problem in the case of pseudomonotone real functions, and a generalized weak Pareto optima problem.

An existence result for the generalized vector equilibrium problem

In this paper, we prove an existence result for the generalized vector equilibrium problem by using Fan-Browder type fixed-point theorem due to [1].

Vector equilibrium problem and vector optimization

This paper examines the vector equilibrium model based on a vector cost consideration. This is a generalization of the well-known Wardrop traffic equilibrium principle where road users choose paths based on just a single cost. The concept of parametric equilibria is introduced and used to establish relations with parametric complementarity and variational inequality problems. Relations with some vector optimization problems via scalarization techniques are given under appropriate conditions. Some solution methods for solving vector equilibrium problems are also discussed.

Existence of Solutions for Generalized Vector Equilibrium Problems

The concepts of aF(C,D)-pseudomonotone mapping and of a (C,D)-pseudomonotone pair of mappings are introduced. By employing Fan's lemma, we establish several existence results for generalized vector equilibrium problems. The new results extend and modify various existence theorems for similar problems.

From Scalar to Vector Equilibrium Problems in the Quasimonotone Case

In a unified approach, existence results for quasimonotone vector equilibrium problems and quasimonotone (multivalued) vector variational inequality problems are derived from an existence result for a scalar equilibrium problem involving two (rather than one) quasimonotone bifunctions. The results in the vector case are not only obtained in a new way, but they are also stronger versions of earlier existence results.

Vector Equilibrium Problems with Generalized Monotone Bifunctions

A vector equilibrium problem is defined as follows: given a closed convex subset K of a real topological Hausdorff vector space and a bifunction F(x, y) valued in a real ordered locally convex vector space, find x *∈K such that $$F(x^* ,y) \nless 0$$ for all y∈K. This problem generalizes the (scalar) equilibrium problem and the vector variational inequality problem. Extending very recent results for these two special cases, the paper establishes existence of solutions for the unifying model, assuming that F is either a pseudomonotone or quasimonotone bifunction.

Vector Equilibrium Problems with Generalized Monotone Bifunctions

Vector Equilibrium Problems with Generalized Monotone Bifunctions