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New Type of Generalized Vector Quasiequilibrium Problem

Author

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  • J. Y. Fu

    (Nanchang University)

  • S. H. Wang

    (Nanchang University)

  • Z. D. Huang

    (Nanchang University)

Abstract

In this paper, we introduce a new type of vector quasiequilibrium problem with set-valued mappings and moving cones. By using the scalarization method and fixed-point theorem, we obtain its existence theorem. As applications, we derive some existence theorems for vector variational inequalities and vector complementarity problems.

Suggested Citation

  • J. Y. Fu & S. H. Wang & Z. D. Huang, 2007. "New Type of Generalized Vector Quasiequilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 643-652, December.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9286-x
    DOI: 10.1007/s10957-007-9286-x
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    References listed on IDEAS

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    1. Jun-Yi Fu & An-Hua Wan, 2002. "Generalized vector equilibrium problems with set-valued mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(2), pages 259-268, November.
    2. Yannelis, Nicholas C. & Prabhakar, N. D., 1983. "Existence of maximal elements and equilibria in linear topological spaces," Journal of Mathematical Economics, Elsevier, vol. 12(3), pages 233-245, December.
    3. Q.H. Ansari & I.V. Konnov & J.C. Yao, 2002. "Characterizations of Solutions for Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 435-447, June.
    4. J. Fu, 1997. "Simultaneous Vector Variational Inequalities and Vector Implicit Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 93(1), pages 141-151, 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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    Cited by:

    1. Pham Huu Sach & Le Anh Tuan, 2022. "Existence of Solutions of Bifunction-Set Optimization Problems in Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 195-225, January.
    2. P. H. Sach & L. J. Lin & L. A. Tuan, 2010. "Generalized Vector Quasivariational Inclusion Problems with Moving Cones," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 607-620, December.
    3. Pham Huu Sach, 2018. "Solution Existence in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 1-16, January.

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