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Existence Results for Nonsmooth Vector Quasi‐Variational‐Like Inequalities

Author

Listed:
  • Mohammed Alshahrani
  • Qamrul Hasan Ansari
  • Suliman Al-Homidan

Abstract

We introduce nonsmooth vector quasi‐variational‐like inequalities (NVQVLI) by means of a bifunction. We establish some existence results for solutions of these inequalities by using Fan‐KKM theorem and a maximal element theorem. By using the technique and methodology adopted in Al‐Homidan et al. (2012), one can easily derive the relations among these inequalities and a vector quasi‐optimization problem. Hence, the existence results for a solution of a vector quasi‐optimization problem can be derived by using our results. The results of this paper extend several known results in the literature.

Suggested Citation

  • Mohammed Alshahrani & Qamrul Hasan Ansari & Suliman Al-Homidan, 2013. "Existence Results for Nonsmooth Vector Quasi‐Variational‐Like Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:376829
    DOI: 10.1155/2013/376829
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    References listed on IDEAS

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    1. 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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