Relationships Between Multiobjective Variational Problems and Vector Variational-type Inequalities with Approximately Star-shaped Functionals

摘要

Abstract In this paper, we shall study the relationships between vector variational-type inequalities and multiobjective variational problems, indulging the concepts of approximately star-shaped functionals and quasi efficiencies. Furthermore, we shall also show the relation of vector critical points of considered variational problem with its local weak quasi efficient solutions, under the approximate pseudo convexity hypothesis. These results are more general than those existing in the literature. Examples are provided to illustrate the derived results.