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Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems

Author

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  • N. J. Huang

    (Sichuan University)

  • J. Li

    (China West Normal University)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

In this paper, a gap function for a system of vector equilibrium problems is introduced and studied. Some necessary and sufficient conditions for the system of vector equilibrium problems are established. Characterizations of the solutions set for the system of vector equilibrium problems are also derived. Furthermore, some existence results of solutions for the system of vector equilibrium problems are proved.

Suggested Citation

  • N. J. Huang & J. Li & J. C. Yao, 2007. "Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 201-212, May.
    • Handle: RePEc:spr:joptap:v:133:y:2007:i:2:d:10.1007_s10957-007-9202-4
    DOI: 10.1007/s10957-007-9202-4
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    References listed on IDEAS

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    Cited by:

    1. J. Li & G. Mastroeni, 2010. "Vector Variational Inequalities Involving Set-valued Mappings via Scalarization with Applications to Error Bounds for Gap Functions," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 355-372, May.
    2. Suhel Ahmad Khan & Jia-Wei Chen, 2015. "Gap Functions and Error Bounds for Generalized Mixed Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 767-776, September.
    3. Jia-Wei Chen & Zhongping Wan & Yeol Cho, 2013. "Levitin–Polyak well-posedness by perturbations for systems of set-valued vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(1), pages 33-64, February.
    4. Bin Chen & Nan-jing Huang, 2013. "Continuity of the solution mapping to parametric generalized vector equilibrium problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1515-1528, August.

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