New results on systems of generalized vector quasi-equilibrium problems

In this paper, we firstly prove the existence of the equilibrium for the generalized abstract economy. We apply these results to show the existence of solutions for systems of vector quasi-equilibrium problems with multivalued trifunctions. Secondly, we consider the generalized strong vector quasi-equilibrium problems and study the existence of their solutions in the case when the correspondences are weakly naturally quasi-concave or weakly biconvex and also in the case of weak-continuity assumptions. In all situations, fixed-point theorems are used.Comment: 24 page

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

Random fixed point theorems under mild continuity assumptions

In this paper, we study the existence of the random fixed points under mild continuity assumptions. The main theorems consider the almost lower semicontinuous operators defined on Frechet spaces and also operators having properties weaker than lower semicontinuity. Our results either extend or improve corresponding ones present in literature.Comment: 15 page