Generalized strong vector quasi-equilibrium problems with variable ordering structure

• Main Authors: Jia-Yu Mao, San-hua Wang, Jin-xia Huang
• Format: Article
• Language: English
• Published: SpringerOpen 2019-04-01
• Series: Journal of Inequalities and Applications
• Subjects: Generalized strong vector quasi-equilibrium problems; Variable ordering structure; Existence of solution; Cosmically upper continuity; Cone-continuity
• Online Access: http://link.springer.com/article/10.1186/s13660-019-2063-1

Abstract In this paper, two kinds of generalized strong vector quasi-equilibrium problems with variable ordering structure are considered by using the concept of cosmically upper continuity rather than upper semi-continuity for cone-valued mapping. Firstly, a key local property of cosmically upper continuity for cone-valued mapping is discussed. Next, under suitable conditions of cone-continuity and cone-convexity for equilibrium mapping, several existence theorems of solutions and closedness of solution sets are established for these two kinds of generalized strong vector quasi-equilibrium problems with variable ordering structure. Moreover, an example is given to illustrate the validity of our theorems. These results obtained in this paper extend and develop some recent works in this field.