Journal of Convex Analysis 19 (2012), No. 4, 1091--1107
Copyright Heldermann Verlag 2012
Stability in Regularized Quasi-Variational Settings
M. Beatrice Lignola
Dip. di Matematica e Applicazioni, Università di Napoli, Via Claudio, 80125 Napoli, Italy
lignola@unina.it
Jacqueline Morgan
Dip. di Matematica e Statistica, Università di Napoli, Via Cinthia, 80126 Napoli, Italy
morgan@unina.it
First, new upper stability results are obtained for parametric quasi-variational and linearized quasi-variational problems using an extension of the classical Minty lemma. Then, we show that lower stability results cannot be achieved in general, even on very restrictive conditions, so we introduce approximate solutions for the above problems and we investigate their lower and upper stability properties.
Keywords: Quasi-variational, pseudomonotone, approximate solution, closed map, lower semicontinuous map.
MSC: 49J40, 49K40, 47J20
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