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October  2017, 13(4): 1685-1699. doi: 10.3934/jimo.2017013

## Continuity of approximate solution maps to vector equilibrium problems

 1 Department of Mathematics, Teacher College, Can Tho University, Can Tho, 900000, Viet Nam 2 Department of Mathematics, Vo Truong Toan University, Hau Giang, Viet Nam 3 Department of Mathematics, Nam Can Tho University, Can Tho, 900000, Viet Nam

* Corresponding author

Received  October 2015 Revised  October 2016 Published  December 2016

Fund Project: This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2014.44.

This paper considers the parametric primal and dual vector equilibrium problems in locally convex Hausdorff topological vector spaces. Based on linear scalarization technique, we establish sufficient conditions for the continuity of approximate solution maps to these problems. As applications, some new results for vector optimization problem and vector variational inequality are derived. Our results are new and improve the existing ones in the literature.

Citation: Lam Quoc Anh, Pham Thanh Duoc, Tran Ngoc Tam. Continuity of approximate solution maps to vector equilibrium problems. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1685-1699. doi: 10.3934/jimo.2017013
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