About Semicontinuity of Set-valued Maps and Stability of Quasivariational Inclusions

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Abstract

We propose several additional kinds of semi-limits and corresponding notions of semicontinuity of a set-valued map. They can be used additionally to known basic concepts of semicontinuity to have a clearer insight of local behaviors of maps. Then, we investigate semicontinuity properties of solution maps to a general parametric quasivariational inclusion, which is shown to include most of optimization-related problems. Consequences are derived for several particular problems. Our results are new or generalize/improve recent existing ones in the literature. © 2014 The Author(s).

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Anh, L. Q., Khanh, P. Q., & Quy, D. N. (2014). About Semicontinuity of Set-valued Maps and Stability of Quasivariational Inclusions. Set-Valued and Variational Analysis, 22(3), 533–555. https://doi.org/10.1007/s11228-014-0276-5

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