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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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
Keywords
- Quasivariational inclusion problems
- Lower and upper semicontinuities
- Hausdorff lower and upper semicontinuities
- U-lower-level closedness
- U-upper-level closedness
- Quasiequilibrium problems
- Quasivariational inequalities
- Traffic network problems