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

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  • Ren-you Zhong

    (Guangxi Normal University)

  • Zhen Dou

    (Guangxi Normal University)

  • Jiang-hua Fan

    (Guangxi Normal University)

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.

Suggested Citation

  • Ren-you Zhong & Zhen Dou & Jiang-hua Fan, 2015. "Degree Theory and Solution Existence of Set-Valued Vector Variational Inequalities in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 527-549, November.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:2:d:10.1007_s10957-015-0731-y
    DOI: 10.1007/s10957-015-0731-y
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    References listed on IDEAS

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    1. Zhong Wang & Nan Huang, 2011. "Degree theory for a generalized set-valued variational inequality with an application in Banach spaces," Journal of Global Optimization, Springer, vol. 49(2), pages 343-357, February.
    2. K. L. Lin & D. P. Yang & J. C. Yao, 1997. "Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 117-125, January.
    3. Kien, B.T. & Wong, M.-M. & Wong, N.C. & Yao, J.C., 2009. "Degree theory for generalized variational inequalities and applications," European Journal of Operational Research, Elsevier, vol. 192(3), pages 730-736, February.
    4. X. X. Huang & Y. P. Fang & X. Q. Yang, 2014. "Characterizing the Nonemptiness and Compactness of the Solution Set of a Vector Variational Inequality by Scalarization," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 548-558, August.
    5. G. Isac & V. V. Kalashnikov, 2001. "Exceptional Family of Elements, Leray–Schauder Alternative, Pseudomonotone Operators and Complementarity," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 69-83, April.
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    Cited by:

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