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

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

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Article ID: iaor20134191
Volume: 158
Issue: 1
Start Page Number: 130
End Page Number: 144
Publication Date: Jul 2013
Journal: Journal of Optimization Theory and Applications
Authors:
Keywords: mapping, Ky Fan inequality, stabillity
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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