On the solution existence of generalized vector quasi-equilibrium problems with discontinuous multifunctions

BT Kien NQ Huy Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43730

Taiwanese Journal of Mathematics, 13, 757-775, 2009
In this paper we deal with the following generalized vector quasi-equilibrium problem: given a closed convex set K in a normed space K , a subset K in a Hausdorff topological vector space K , and a closed convex cone K in K . Let K , K be two multifunctions and K be a single-valued mapping. Find a point K such that\begin {gather}(\hat x,\hat y)\in\Gamma (\hat x)\times\Phi (\hat x),\,\,{\rm and}\,\,\{f (\hat x,\hat y, z): z\in\Gamma (\hat x)\}\cap (-{\rm Int} C)=\emptyset.\notag\end {gather} We prove some existence theorems for the problem in which K can be discontinuous and K can be unbounded.
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@inproceedings{bt2009on,
  title={On the solution existence of generalized vector quasi-equilibrium problems with discontinuous multifunctions},
  author={BT Kien, NQ Huy, and Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020212158586197259},
  booktitle={Taiwanese Journal of Mathematics},
  volume={13},
  pages={757-775},
  year={2009},
}
BT Kien, NQ Huy, and Ngai-Ching Wong. On the solution existence of generalized vector quasi-equilibrium problems with discontinuous multifunctions. 2009. Vol. 13. In Taiwanese Journal of Mathematics. pp.757-775. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020212158586197259.
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