Vector Variational-like Inequalities Research Articles

The existence theorems of solutions for generalized vector-valued variational-like inequalities

The purpose of this paper is to introduce a new kind of variational inequality, a ‘generalized vector variational-like inequality’ which includes several classical and well-known variational inequalities as special cases. As an application of the Knaster-Kuratowski-Mazurkiewicz principle as extended by Fan in 1961 [1], we prove that there exist solutions for our generalized vector variational-like inequality under reasonable hypotheses. These results generalize corresponding results given by Chen et al. in [2], Giannessi [3], Harker and Pang [4], Hartman and Stampacchia [5], Isac [6], Lee et al. [7], Noor [8], Saigal [9], Siddiqi et al. [10], and Yang [11].

Existence of Solutions for Vector Optimization Problems

We define the generalized efficient solution which is more general than the weakly efficient solution for vector optimization problems, and prove the existence of the generalized efficient solution for nondifferentiable vector optimization problems by using vector variational-like inequalities for set-valued maps.

Some Remarks On Vector Optimization Problems

We prove the existence of a weak minimum for vector optimization problems by means of a vector variational-like inequality and preinvex mappings.

A Note On Generalized Vector Variational-Like Inequalities

In this paper, we consider the generalized vector variational-like inequalities and prove the existence of their solutions in the setting of Hausdorff topological vector spaces and H-spaces

Existence of solutions for vector optimization

In this paper, we prove the existence of a weak minimum for constrained vector optimization problem by making use of vector variational-like inequality and preinvex functions.