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Existence Results for Nonsmooth Vector Quasi-Variational-Like Inequalities

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  • 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, Hindawi, vol. 2013, pages 1-7, September.
    • Handle: RePEc:hin:jnlaaa:376829
    DOI: 10.1155/2013/376829
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