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On the existence and stability of approximate solutions of perturbed vector equilibrium problems. (English) Zbl 1136.49013

Summary: We consider several concepts of approximate minima of a set in normed vector spaces and we provide some results concerning the stability of these minima under perturbation of the underlying set with a sequence of sets converging in the sense of Painlevé-Kuratowski to the initial set. Then, we introduce the concept of approximate solution for equilibrium problem governed by set-valued maps and we study the stability of these solutions. The particular case of linear continuous operators is considered as well.

MSC:

49J53 Set-valued and variational analysis
49K40 Sensitivity, stability, well-posedness
54E55 Bitopologies
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