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On Implicit Vector Variational Inequalities

Author

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  • G. M. Lee

    (Pukyong National University)

  • S. H. Kum

    (Korea Maritime University)

Abstract

In this paper, we study the existence of solutions of implicit vector variational inequalities for multifunctions. Generalized pseudomonotonicity concepts are introduced. Our results extend and unify corresponding earlier existence results of many authors for vector variational inequalities under the Hausdorff topological vector space setting.

Suggested Citation

  • G. M. Lee & S. H. Kum, 2000. "On Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 409-425, February.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:2:d:10.1023_a:1004617914993
    DOI: 10.1023/A:1004617914993
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    References listed on IDEAS

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    1. K. L. Lin & D. P. Yang & J. C. Yao, 1997. "Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 117-125, January.
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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. P. Q. Khanh & N. H. Quan, 2010. "Existence Results for General Inclusions Using Generalized KKM Theorems with Applications to Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 640-653, September.
    3. M.H. Kim & S.H. Kum & G.M. Lee, 2002. "Vector Variational Inequalities Involving Vector Maximal Points," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 593-607, September.
    4. N. X. Hai & P. Q. Khanh, 2007. "Systems of Set-Valued Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 55-67, October.
    5. Nguyen Hai & Phan Khanh & Nguyen Quan, 2009. "On the existence of solutions to quasivariational inclusion problems," Computational Optimization and Applications, Springer, vol. 45(4), pages 565-581, December.
    6. N. X. Hai & P. Q. Khanh, 2007. "Existence of Solutions to General Quasiequilibrium Problems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 317-327, June.
    7. X. P. Ding & J. Y. Park, 2004. "Generalized Vector Equilibrium Problems in Generalized Convex Spaces," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 327-353, February.
    8. S. Al-Homidan & Q. H. Ansari & S. Schaible, 2007. "Existence of Solutions of Systems of Generalized Implicit Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 515-531, September.
    9. 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.

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