We consider an extension of the notion of Tykhonov well-posedness for perturbed vector quasi-equilibrium problems. We establish some necessary and sufficient conditions for verifying these well-posedness properties. As for applications of our results, the Tykhonov well-posedness of vector variational-like inequalities and vector optimization problems are established

In this paper, we introduce and study a class of generalized (weak) vector variational-like inequalities and show the existence of solutions to them by Brouwer’s fixed point theorem and Fan’s lemma.

This paper is devoted to the existence of solutions for generalized variational like inequalities with fuzzy mappings in topological vector spaces by using a particular form of the generalized KKM-Theorem.

This work is devoted to examining inverse vector variational inequalities with constraints by means of a prominent nonlinear scalarizing functional. We show that inverse vector variational inequalities are equivalent to multiobjective optimization problems with a variable domination structure. Moreover, we introduce a nonlinear function based on a well-known nonlinear scalarization function. We...

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.

in this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in hilbert spaces.

The object of this paper is to establish an existence result for nonlinear inequalities for not necessarily pseudomonotone maps. As a consequence of our result, we give some existence results for variational and variational-like inequalities. Keywords– Nonlinear inequalities, variational inequality problems, variational-like inequality problems, fixed points.