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Variational-Like Inequalities for Weakly Relaxed Pseudomonotone Set-Valued Mappings in Banach Space

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  • Syed Shakaib Irfan
  • Mohammad Firdosh Khan

Abstract

We introduce and study variational-like inequalities for generalized pseudomonotone set-valued mappings in Banach spaces. By using KKM technique, we obtain the existence of solutions for variational-like inequalities for generalized pseudomonotone set-valued mappings in reflexive Banach spaces. The results presented in this paper are generalizations and improvements of the several well-known results in the literature.

Suggested Citation

  • Syed Shakaib Irfan & Mohammad Firdosh Khan, 2016. "Variational-Like Inequalities for Weakly Relaxed Pseudomonotone Set-Valued Mappings in Banach Space," International Journal of Analysis, Hindawi, vol. 2016, pages 1-6, September.
    • Handle: RePEc:hin:ijanal:4760839
    DOI: 10.1155/2016/4760839
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    References listed on IDEAS

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    1. 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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