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Set-Valued Symmetric Generalized Strong Vector Quasi-Equilibrium Problems with Variable Ordering Structures

Author

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  • Jing-Nan Li

    (Department of Mathematics, Nanchang University, Nanchang 330031, China)

  • San-Hua Wang

    (Department of Mathematics, Nanchang University, Nanchang 330031, China
    Post-Doctor Station of Management Science and Engineering, Nanchang University, Nanchang 330031, China)

  • Yu-Ping Xu

    (Department of Mathematics, Nanchang University, Nanchang 330031, China)

Abstract

In this paper, two types of set-valued symmetric generalized strong vector quasi-equilibrium problems with variable ordering structures are discussed. By using the concept of cosmically upper continuity rather than the one of upper semicontinuity for cone-valued mapping, some existence theorems of solutions are established under suitable assumptions of cone-continuity and cone-convexity for the equilibrium mappings. Moreover, the results of compactness for solution sets are proven. As applications, some existence results of strong saddle points are obtained. The main results obtained in this paper unify and improve some recent works in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1604-:d:415000
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    References listed on IDEAS

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    1. 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.
    2. N. X. Tan, 2004. "On the Existence of Solutions of Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 619-638, December.
    3. 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.
    4. 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.
    5. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
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