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

Ren-you Zhong, Zhen Dou and Jiang-hua Fan ()
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Ren-you Zhong: Guangxi Normal University
Zhen Dou: Guangxi Normal University
Jiang-hua Fan: Guangxi Normal University

Journal of Optimization Theory and Applications, 2015, vol. 167, issue 2, No 6, 527-549

Abstract: 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.

Keywords: Set-valued vector variational inequality; Topological degree; Existence of solutions; Nonempty and boundedness; $$C$$ C -pseudomonotone mapping; 49J40; 90C31 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-015-0731-y

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