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Stability of solution mappings for parametric bilevel vector equilibrium problems

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Abstract

In this paper, we first revisit the parametric bilevel vector equilibrium problems in Hausdorff topological vector spaces. Then we study the stability conditions such as (Hausdorff) upper semicontinuity, (Hausdorff) lower semicontinuity, outer-continuity and outer-openness of solutions for such problems. Many examples are provided to illustrate the essentialness of the imposed assumptions. For the applications, we obtain the stability results for the parametric vector variational inequality problems with equilibrium constraints and parametric vector optimization problems with equilibrium constraints.

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2017.18. The authors wish to thank the two referees for their valuable comments and suggestions that helped to significantly improve the paper.

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Correspondence to Nguyen Van Hung.

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Communicated by José Mario Martínez.

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Anh, L.Q., Van Hung, N. Stability of solution mappings for parametric bilevel vector equilibrium problems. Comp. Appl. Math. 37, 1537–1549 (2018). https://doi.org/10.1007/s40314-016-0411-z

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  • DOI: https://doi.org/10.1007/s40314-016-0411-z

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