On the generalized vector F-implicit complementarity problems and vector F-implicit variational inequality problems

In this paper, we introduce and analyze some new classes of generalized vector-F implicit complementarity problems and the general mixed vector-F variational inequalities. Under suitable conditions, we prove the equivalences between these new problems. We establish several existence theorems for these classes of vector-F complementarity and general mixed vector-F variational inequalities using a new version of the Fan-KKM theorem in Hausdorff topological vector spaces, and without even using the classical assumptions in this context, like monotonicity or continuity. Results obtained in this paper represent significant improvement and refinement of the previously known results

Gap functions and existence of solutions to generalized vector variational inequalities

AbstractIn this paper, the gap function for a new class of generalized vector variational inequalities with point-to-set mappings (for short, GVVI) is introduced and the necessary and sufficient conditions for the GVVI are established. In order to derive the existence of solutions for the GVVI, we also introduce the concept of η-h-C(x)-pseudomonotonicity. By considering the existence of solutions for vector variational inequalities (for short, VVI) with a single-valued function and a continuous selection theorem, we obtain the existence theorem for the GVVI under the assumption of η-h-C(x)-pseudomonotonicity. The results presented in this paper extend and unify corresponding results of other authors

Fuzzy games with a countable space of actions and applications to systems of generalized quasi-variational inequalities

In this paper, we introduce an abstract fuzzy economy (generalized fuzzy game) model with a countable space of actions and we study the existence of the fuzzy equilibrium. As applications, two types of results are obtained. The first ones concern the existence of the solutions for systems of generalized quasi-variational inequalities with random fuzzy mappings which we define. The last ones are new random fixed point theorems for correspondences with values in complete countable metric spaces.Comment: 18 page

Variational inequalities characterizing weak minimality in set optimization

We introduce the notion of weak minimizer in set optimization. Necessary and sufficient conditions in terms of scalarized variational inequalities of Stampacchia and Minty type, respectively, are proved. As an application, we obtain necessary and sufficient optimality conditions for weak efficiency of vector optimization in infinite dimensional spaces. A Minty variational principle in this framework is proved as a corollary of our main result.Comment: Includes an appendix summarizing results which are submitted but not published at this poin