Abstract
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.
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Acknowledgments
This work was supported by the National Natural Science Foundation of China (11061006, 11226224 and 61363036), the Program for Excellent Talents in Guangxi Higher Education Institutions, the Guangxi Natural Science Foundation (2012GXNSFBA053008), the Initial Scientific Research Foundation for Ph.D. of Guangxi Normal University, and the Innovation Project of Guangxi Graduate Education (YCSZ2014088).
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Communicated by Jen-Chih Yao.
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Zhong, Ry., Dou, Z. & Fan, Jh. Degree Theory and Solution Existence of Set-Valued Vector Variational Inequalities in Reflexive Banach Spaces. J Optim Theory Appl 167, 527–549 (2015). https://doi.org/10.1007/s10957-015-0731-y
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DOI: https://doi.org/10.1007/s10957-015-0731-y
Keywords
- Set-valued vector variational inequality
- Topological degree
- Existence of solutions
- Nonempty and boundedness
- \(C\)-pseudomonotone mapping