Degree Theory and Solution Existence of Set-Valued Vector Variational Inequalities in Reflexive Banach Spaces

作者：Zhong, Ren-you; Dou, Zhen; Fan, Jiang-hua^*

来源：Journal of Optimization Theory and Applications, 2015, 167(2): 527-549.

DOI：10.1007/s10957-015-0731-y

• Set-valued vector variational inequality
• Topological degree
• Existence of solutions
• Nonempty and boundedness
• C-pseudomonotone mapping

In this paper, a degree theory for set-valued vector variational inequalities is built in reflexive Banach spaces. By using the method of degree theory, some existence results of solutions for set-valued vector variational inequalities are established under suitable conditions. Furthermore, some equivalent characterizations for the nonemptiness and boundedness of solution sets to single-valued vector variational inequalities are obtained under pseudomonotonicity assumption. To the best of our knowledge, there are still no papers dealing with the degree theory for vector variational inequalities.

• 出版日期2015-11
• 单位广西师范大学