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System of Vector Equilibrium Problems and Its Applications

Author

Listed:
  • Q. H. Ansari

    (Aligarh Muslim University)

  • S. Schaible

    (University of California)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

In this paper, we introduce a system of vector equilibrium problems andprove the existence of a solution. As an application, we derive someexistence results for the system of vector variational inequalities. We alsoestablish some existence results for the system of vector optimizationproblems, which includes the Nash equilibrium problem as a special case.

Suggested Citation

  • Q. H. Ansari & S. Schaible & J. C. Yao, 2000. "System of Vector Equilibrium Problems and Its Applications," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 547-557, December.
    • Handle: RePEc:spr:joptap:v:107:y:2000:i:3:d:10.1023_a:1026495115191
    DOI: 10.1023/A:1026495115191
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    References listed on IDEAS

    as
    1. N. Hadjisavvas & S. Schaible, 1998. "From Scalar to Vector Equilibrium Problems in the Quasimonotone Case," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 297-309, February.
    2. Yu, Jian, 1999. "Essential equilibria of n-person noncooperative games," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 361-372, April.
    3. 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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    Citations

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    Cited by:

    1. Elena Molho & Domenico Scopelliti, 2023. "On the study of multistage stochastic vector quasi-variational problems," Journal of Global Optimization, Springer, vol. 86(4), pages 931-952, August.
    2. Ali Farajzadeh & Byung Soo Lee & Somyot Plubteing, 2016. "On Generalized Quasi-Vector Equilibrium Problems via Scalarization Method," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 584-599, February.
    3. L. J. Lin & Y. H. Liu, 2006. "Existence Theorems for Systems of Generalized Vector Quasiequilibrium Problems and Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 463-477, September.
    4. Q. H. Ansari & L. J. Lin & L. B. Su, 2005. "Systems of Simultaneous Generalized Vector Quasiequilibrium Problems and their Applications," Journal of Optimization Theory and Applications, Springer, vol. 127(1), pages 27-44, October.
    5. Csaba Farkas & Andrea Éva Molnár, 2013. "A Generalized Variational Principle and Its Application to Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 213-231, February.
    6. 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.
    7. 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.
    8. Monica Bianchi & Siegfried Schaible, 2004. "Equilibrium Problems under Generalized Convexity and Generalized Monotonicity," Journal of Global Optimization, Springer, vol. 30(2), pages 121-134, November.
    9. Suhel Ahmad Khan, 2014. "System of Operator Quasi Equilibrium Problems," International Journal of Analysis, Hindawi, vol. 2014, pages 1-6, June.

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