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Stability of approximating solutions to parametric bilevel vector equilibrium problems and applications

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Abstract

In this paper, we establish sufficient conditions for the approximate solution mappings of parametric bilevel equilibrium problems with stability properties such as upper semicontinuity, lower semicontinuity, Hausdorff lower semicontinuity, continuity and Hausdorff continuity. Moreover, we also apply these results to parametric traffic network problems with equilibrium constraints. Many examples are provided to ensure the essentialness of the assumptions.

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Acknowledgements

This research was supported by the Ministry of Education and Training of Vietnam under grant number B2019.SPD02. The authors wish to thank the referees for their valuable remarks and suggestions that helped to improve the presentation of the paper.

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Authors and Affiliations

  1. Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen Van Hung

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen Van Hung

  3. Department of Mathematical Economics, Banking University of Ho Chi Minh City, Ho Chi Minh City, Vietnam

    Nguyen Minh Hai

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  1. Nguyen Van Hung
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  2. Nguyen Minh Hai
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Correspondence to Nguyen Van Hung.

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Communicated by Orizon Pereira Ferreira.

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Van Hung, N., Hai, N.M. Stability of approximating solutions to parametric bilevel vector equilibrium problems and applications. Comp. Appl. Math. 38, 57 (2019). https://doi.org/10.1007/s40314-019-0823-7

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  • DOI: https://doi.org/10.1007/s40314-019-0823-7

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