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Generalized vector quasi-equilibrium problems

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  • Jun-Yi Fu

Abstract

The properly quasi-convexity of multivalued mappings in an ordered vector space is introduced. Existence theorems for generalized vector quasi-equilibrium problems and multivalued vector equilibrium problems are obtained. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Jun-Yi Fu, 2000. "Generalized vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 57-64, September.
    • Handle: RePEc:spr:mathme:v:52:y:2000:i:1:p:57-64
    DOI: 10.1007/s001860000058
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    Citations

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    Cited by:

    1. X. H. Gong, 2007. "Connectedness of the Solution Sets and Scalarization for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 151-161, May.
    2. Qiuying Li & Sanhua Wang, 2021. "Arcwise Connectedness of the Solution Sets for Generalized Vector Equilibrium Problems," Mathematics, MDPI, vol. 9(20), pages 1-9, October.
    3. Jing-Nan Li & San-Hua Wang & Yu-Ping Xu, 2020. "Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures," Mathematics, MDPI, vol. 8(9), pages 1-17, September.
    4. M. Balaj & L. J. Lin, 2011. "Generalized Variational Relation Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(1), pages 1-13, January.
    5. Xin Xu & Yang Dong Xu, 2019. "Connectedness and Path Connectedness of Weak Efficient Solution Sets of Vector Optimization Problems via Nonlinear Scalarization Methods," Mathematics, MDPI, vol. 7(10), pages 1-10, October.
    6. Y. Chiang & O. Chadli & J.C. Yao, 2003. "Existence of Solutions to Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 116(2), pages 251-264, February.
    7. R. P. Agarwal & M. Balaj & D. O’Regan, 2012. "A Unifying Approach to Variational Relation Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 417-429, November.
    8. Y. Chiang & O. Chadli & J. Yao, 2004. "Generalized Vector Equilibrium Problems with Trifunctions," Journal of Global Optimization, Springer, vol. 30(2), pages 135-154, November.
    9. M. Balaj & L. J. Lin, 2013. "Existence Criteria for the Solutions of Two Types of Variational Relation Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 232-246, February.
    10. Yu Han & Nan-jing Huang, 2018. "Existence and Connectedness of Solutions for Generalized Vector Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 65-85, October.
    11. X. Gong, 2007. "Symmetric strong vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 305-314, April.
    12. Jian-Wen Peng & Soon-Yi Wu & Yan Wang, 2012. "Levitin-Polyak well-posedness of generalized vector quasi-equilibrium problems with functional constraints," Journal of Global Optimization, Springer, vol. 52(4), pages 779-795, April.
    13. N. X. Hai & P. Q. Khanh, 2007. "Existence of Solutions to General Quasiequilibrium Problems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 317-327, June.
    14. Junyi Fu & Sanhua Wang, 2013. "Generalized strong vector quasi-equilibrium problem with domination structure," Journal of Global Optimization, Springer, vol. 55(4), pages 839-847, April.
    15. 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.
    16. N. X. Hai & P. Q. Khanh, 2007. "Systems of Set-Valued Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 55-67, October.
    17. N. Minh & N. Tan, 2006. "On the Existence of Solutions of Quasi-equilibrium Problems with Constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 17-31, August.
    18. E. E. A. Batista & G. C. Bento & O. P. Ferreira, 2015. "An Existence Result for the Generalized Vector Equilibrium Problem on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 550-557, November.
    19. S. H. Hou & X. H. Gong & X. M. Yang, 2010. "Existence and Stability of Solutions for Generalized Ky Fan Inequality Problems with Trifunctions," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 387-398, August.

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