On system of vector quasi-equilibrium problems for multivalued mappings

Abstract

In this paper, the notion of the vector quasiconcavity and lower vector continuity for multivalued mappings without using the algebraic structure are introduced. By applying these definitions and maximal element lemma, some existence theorems of the solution of the system of vector quasi-equilibrium problems for a family of multivalued mappings in the setting of topological order spaces are established. The results of this note improve and generalize the corresponding results in the literature, specially references [2, 6, 9-11, 23].

S-derivative of perturbed mapping and solution mapping for parametric vector equilibrium problems

“…We mention that our results in Theorem 3.1 and Theorem 3.2 are new, and therefore they do not coincide with the existing ones in the literature (see [28][29][30] and the cited references therein).…”

On generalized common quasi-eigenvector problems

“…Therefore, KKM theory plays a key role in studying the existence of solutions. For more information regarding these topics, we refer to [15,16,17,18,19,20]. In this paper, we continue these lines by replacing the identity function with a new function and we call our problems generalized common quasi-eigenvector problems.…”