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On F-Implicit Generalized Vector Variational Inequalities

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  • Y. C. Lin

    (China Medical University)

Abstract

In this paper, we study the F-implicit generalized (weak) case for vector variational inequalities in real topological vector spaces. Both weak and strong solutions are considered. These two sets of solutions coincide whenever the mapping T is single-valued, but not set-valued. We use the Ferro minimax theorem to discuss the existence of strong solutions for F-implicit generalized vector variational inequalities.

Suggested Citation

  • Y. C. Lin, 2009. "On F-Implicit Generalized Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 557-568, September.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:3:d:10.1007_s10957-009-9543-2
    DOI: 10.1007/s10957-009-9543-2
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    References listed on IDEAS

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    1. X.Q. Yang & J.C. Yao, 2002. "Gap Functions and Existence of Solutions to Set-Valued Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 407-417, November.
    2. 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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