Abstract
This article aims to demonstrate the existence of new solutions for the vector quasi-equilibrium problems. Firstly we prove the existence of the equilibrium for the generalized abstract economy model under upper semicontinuity assumptions. By using these results, we solve the announced problem in case of multivalued trifunctions. Secondly, we consider the generalized strong vector quasi-equilibrium problem and prove the existence of its solutions in case of correspondences being weakly naturally quasi-concave or weakly biconvex and also in case of weak-continuity assumptions. In all situations, our theoretical analysis is based on fixed-point theorems. Our study indicates that the refinement of the hypotheses concerning the equilibrium problems plays an important role in the developing of this theory and it improves, by its novelty, the existent results obtained so far in literature.
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