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Semicontinuity of Solution Sets to Parametric Quasivariational Inclusions with Applications to Traffic Networks I: Upper Semicontinuities

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Abstract

We propose some notions related to semicontinuity of a multivalued mapping and provide a clear insight for various semicontinuity-related definitions. We establish verifiable sufficient conditions for solution sets of general quasivariational inclusion problems to have these semicontinuity-related properties. Our results are proved to include and improve recent ones in the literature by corollaries and examples. Part I is devoted to upper semicontinuity properties of solution sets. Part II discusses lower semicontinuities of these sets and applications, where we discuss in details a traffic network problem as a sample for employing the main results in practical situations

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Authors and Affiliations

  1. Department of Mathematics, Teacher College, Cantho University, Cantho, Vietnam

    Lam Quoc Anh

  2. Department of Mathematics, International University of Hochiminh City, Khu pho 6, Linh Trung, Thu Duc, Hochiminh City, Vietnam

    Phan Quoc Khanh

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  1. Lam Quoc Anh
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  2. Phan Quoc Khanh
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Correspondence to Phan Quoc Khanh.

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Dedicated to Professor Boris S. Mordukhovich.

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Anh, L.Q., Khanh, P.Q. Semicontinuity of Solution Sets to Parametric Quasivariational Inclusions with Applications to Traffic Networks I: Upper Semicontinuities. Set-Valued Anal 16, 267–279 (2008). https://doi.org/10.1007/s11228-008-0074-z

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  • DOI: https://doi.org/10.1007/s11228-008-0074-z

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