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Generalized strong vector quasi-equilibrium problem with domination structure

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  • Junyi Fu
  • Sanhua Wang

Abstract

In this paper, a generalized strong vector quasi-equilibrium problem with set-valued mapping and domination structure is presented, and under the condition of cone-continuity, existence of solutions and the compactness of solution set are established. As applications, existence of solutions for strong vector F-implicit variational inequality problem and strong vector F-implicit complementarity problem is derived, and Khan’s main results are corrected. Copyright Springer Science+Business Media, LLC. 2013

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  • 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.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:4:p:839-847
    DOI: 10.1007/s10898-012-9889-0
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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.
    6. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585.
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    Cited by:

    1. M. Darabi & J. Zafarani, 2015. "Tykhonov Well-Posedness for Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 458-479, May.
    2. Ravi P. Agarwal & Mircea Balaj & Donal O’Regan, 2018. "Intersection Theorems with Applications in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 761-777, December.

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