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Title of Journal: J Optim Theory Appl

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Abbravation: Journal of Optimization Theory and Applications

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Springer US

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DOI

10.1007/978-3-642-47596-2

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1573-2878

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Closedness of the Solution Map in Quasivariational

Authors: Massimiliano Giuli
Publish Date: 2012/11/13
Volume: 158, Issue: 1, Pages: 130-144
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Abstract

This paper is mainly concerned with the stability analysis of the setvalued 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 Mintytype 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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