The analysis of the connections among generalized systems, Vector Optimization Problems and Variational Inequalities allows to deepen the study of the properties of the Minty Vector Variational Inequality. In particular, under suitable regularity assumptions,the equivalence between Minty Vector Variational Inequality and Stampacchia Vector Variational Inequality is shown.

The purpose of this paper is to introduce and study a new class of generalized vector variational-like inequalities and generalized vector variational inequalities in fuzzy environment. By using the KKM-technique, Maximal Element Lemma and under suitable conditions, some existence theorems of solutions for these two kinds of vector variational inequalities in fuzzy environment are proved. The r...

In this paper, we introduce and study a generalized class of vector implicit quasi complementarity problem and the corresponding vector implicit quasi variational inequality problem. By using Fan-KKM theorem, we derive existence of solutions of generalized vector implicit quasi variational inequalities without any monotonicity assumption and establish the equivalence between those problems in B...

In this paper, we present the concept of generalized invexity for vector-valued functions. Also, we consider different kinds of generalized vector variational-like inequality and a vector optimization problem. Some relations between vector variational-like inequalities and a vector optimization problem are established by using the properties of Mordukhovich limiting subdifferential. Acknowledge...

Solvabilities of generalized vector variational-type inequalities (GVVTI) are discussed in this work. First, the solvability of GVVTI without monotone assumption for mappings is considered in (reflexive) Banach spaces by using Brouwer fixed point theorem (Browder fixed point theorem). Second, the solvability of GVVTI with monotone assumption for mappings is considered in reflexive Banach spaces...

Some existence theorems of solutions of a new class of generalized vector F-implicit complementarity problems with the corresponding generalized vector F-implicit variational inequality problems were established.

This paper deals with the abstract generalized vector quasi-equilibrium problem in noncompact Hadamard manifolds. We prove the existence of solutions to the abstract generalized vector quasi-equilibrium problem under suitable conditions and provide applications to an abstract vector quasi-equilibrium problem, a generalized scalar equilibrium problem, a scalar equilibrium problem, and a perturbe...