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Existence and Stability of Solutions for Generalized Ky Fan Inequality Problems with Trifunctions

Author

Listed:
  • S. H. Hou

    (Hong Kong Polytechnic University)

  • X. H. Gong

    (Nanchang University)

  • X. M. Yang

    (Chongqing Normal University)

Abstract

In this paper, an existence theorem for solutions to the generalized Ky Fan Inequality problem is obtained by means of the Kakutani-Fan-Glicksberg fixed-point theorem without imposing the condition that the dual of the ordering cone has a weak* compact base. In addition, the stability of the solution set is shown.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:2:d:10.1007_s10957-010-9656-7
    DOI: 10.1007/s10957-010-9656-7
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    References listed on IDEAS

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    1. 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.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
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    4. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. Zaiyun Peng & Ziyuan Wang & Xinmin Yang, 2020. "Connectedness of Solution Sets for Weak Generalized Symmetric Ky Fan Inequality Problems via Addition-Invariant Sets," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 188-206, April.
    4. R. P. Agarwal & M. Balaj & D. O’Regan, 2014. "A Common Fixed Point Theorem with Applications," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 482-490, November.
    5. 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.
    6. 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.
    7. S. J. Li & Z. M. Fang, 2010. "Lower Semicontinuity of the Solution Mappings to a Parametric Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 507-515, December.
    8. Zai-Yun Peng & Jian-Wen Peng & Xian-Jun Long & Jen-Chih Yao, 2018. "On the stability of solutions for semi-infinite vector optimization problems," Journal of Global Optimization, Springer, vol. 70(1), pages 55-69, January.

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