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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, UniversitÓ di Napoli, Via Claudio, 80125 Napoli, Italy

Jacqueline Morgan
Dip. di Matematica e Statistica, UniversitÓ di Napoli, Via Cinthia, 80126 Napoli, Italy

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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