New results on systems of generalized vector quasi-equilibrium problems

TL;DR

This paper establishes the existence of solutions for systems of generalized vector quasi-equilibrium problems using fixed-point theorems, extending results to cases with multivalued trifunctions and weak continuity conditions.

Contribution

It introduces new existence results for generalized vector quasi-equilibrium problems, including cases with weakly naturally quasi-concave and weakly biconvex correspondences.

Findings

Existence of equilibrium in generalized abstract economies.

Solutions for systems with multivalued trifunctions.

Results under weak continuity and quasi-concavity assumptions.

Abstract

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.