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Vector Variational-Like Inequalities with Generalized Semimonotone Mappings

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  • Suhel Ahmad Khan

Abstract

We introduce the concepts of generalized relaxed monotonicity and generalized relaxed semimonotonicity. We consider a class of generalized vector variationa-llike inequality problem involving generalized relaxed semimonotone mapping. By using Kakutani-Fan-Glicksberg’s fixed-point theorem, we prove the solvability for this class of vector variational-like inequality with relaxed monotonicity assumptions. The results presented in this paper generalize some known results for vector variational inequality in recent years.

Suggested Citation

  • Suhel Ahmad Khan, 2013. "Vector Variational-Like Inequalities with Generalized Semimonotone Mappings," International Journal of Analysis, Hindawi, vol. 2013, pages 1-7, January.
    • Handle: RePEc:hin:ijanal:762380
    DOI: 10.1155/2013/762380
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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.
    2. Y.P. Fang & N.J. Huang, 2003. "Variational-Like Inequalities with Generalized Monotone Mappings in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 327-338, August.
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