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Hausdorff continuity of approximate solution maps to parametric primal and dual equilibrium problems

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Abstract

In this paper, we consider parametric primal and dual equilibrium problems in locally convex Hausdorff topological vector spaces. Sufficient conditions for the approximate solution maps to be Hausdorff continuous are established. We provide many examples to illustrate the essentialness of the imposed assumptions. As applications of these results, the Hausdorff continuity of the approximate solution maps for optimization problems, variational inequalities and fixed-point problems are derived.

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Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2014.44. The authors would like to thank two anonymous referees for their valuable remarks and suggestions, which helped to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Teacher College, Can Tho University, Can Tho, Vietnam

    Lam Quoc Anh

  2. Department of Mathematics, Teacher College, Nam Can Tho University, Can Tho, Vietnam

    Tran Ngoc Tam

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  1. Lam Quoc Anh
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  2. Tran Ngoc Tam
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Correspondence to Lam Quoc Anh.

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Anh, L.Q., Tam, T.N. Hausdorff continuity of approximate solution maps to parametric primal and dual equilibrium problems. TOP 24, 242–258 (2016). https://doi.org/10.1007/s11750-015-0390-z

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