Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Quasi-variational
  • pseudomonotone
  • approximate solution
  • closed map
  • lower semicontinuous map

Mathematics Subject Classification

49J40, 49K40, 47J20

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Suggested citation

M. B. Lignola, J. Morgan. “Stability in Regularized Quasi-Variational Settings.” Journal of Convex Analysis 19 (2012), No. 4, 1091–1107. https://doi.org/10.68381/jca19058

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press.