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Continuity of the solution mapping to parametric generalized vector equilibrium problems

Author

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  • Bin Chen
  • Nan-jing Huang

Abstract

In this paper, two kinds of parametric generalized vector equilibrium problems in normed spaces are studied. The sufficient conditions for the continuity of the solution mappings to the two kinds of parametric generalized vector equilibrium problems are established under suitable conditions. The results presented in this paper extend and improve some main results in Chen and Gong (Pac J Optim 3:511–520, 2010 ), Chen and Li (Pac J Optim 6:141–152, 2010 ), Chen et al. (J Glob Optim 45:309–318, 2009 ), Cheng and Zhu (J Glob Optim 32:543–550, 2005 ), Gong (J Optim Theory Appl 139:35–46, 2008 ), Li and Fang (J Optim Theory Appl 147:507–515, 2010 ), Li et al. (Bull Aust Math Soc 81:85–95, 2010 ) and Peng et al. (J Optim Theory Appl 152(1):256–264, 2011 ). Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:4:p:1515-1528
    DOI: 10.1007/s10898-012-9904-5
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    References listed on IDEAS

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    1. 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.
    2. Q. H. Ansari & I. V. Konnov & J. C. Yao, 2001. "Existence of a Solution and Variational Principles for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 481-492, September.
    3. X. H. Gong, 2008. "Continuity of the Solution Set to Parametric Weak Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 35-46, October.
    4. X. H. Gong & J. C. Yao, 2008. "Lower Semicontinuity of the Set of Efficient Solutions for Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 197-205, August.
    5. Jia Chen & Yeol Cho & Jong Kim & Jun Li, 2011. "Multiobjective optimization problems with modified objective functions and cone constraints and applications," Journal of Global Optimization, Springer, vol. 49(1), pages 137-147, January.
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    Cited by:

    1. Tran Ngoc Tam, 2022. "On Hölder continuity of solution maps to parametric vector Ky Fan inequalities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 77-94, April.

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