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Closedness of the Solution Map in Quasivariational Inequalities of Ky Fan Type

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Abstract

This paper is mainly concerned with the stability analysis of the set-valued solution mapping for a parametric quasivariational inequality of Ky Fan type. Perturbations are here considered both on the bifunction and on the constraint map which define the problem. The bifunction is assumed to be either pseudomonotone or quasimonotone. This fact leads to the definition of four different types of solution: two when the bifunction is pseudomonotone, and two for the quasimonotone case. These solution sets are connected each other through two Minty-type Lemmas, where a very weak form of continuity for the bifunction is employed. Using these results, we are able to establish some sufficient conditions, which ensure the closedness and the upper semicontinuity of the maps corresponding to the four solution sets.

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  1. Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, L’Aquila, Italy

    Massimiliano Giuli

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  1. Massimiliano Giuli
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Correspondence to Massimiliano Giuli.

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Giuli, M. Closedness of the Solution Map in Quasivariational Inequalities of Ky Fan Type. J Optim Theory Appl 158, 130–144 (2013). https://doi.org/10.1007/s10957-012-0221-4

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  • DOI: https://doi.org/10.1007/s10957-012-0221-4

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