Open covering and metric regularity are properties playing a crucial role in several topics of modern variational analysis. Here their stability behaviour in the presence of perturbations is investigated in a purely metric setting. Some results in this sense are obtained, which lead to extend the known Milyutin theorem, and then to expand the concept of radius of regularity, a quantitative measure of the open covering stability. Estimations for the latter in terms of covering moduli are provided. © 2011 Springer Science+Business Media B.V.
Uderzo, A. (2012). A Metric Version of Milyutin Theorem. SET-VALUED AND VARIATIONAL ANALYSIS, 20(2), 279-306 [10.1007/s11228-011-0193-9].
A Metric Version of Milyutin Theorem
UDERZO, AMOS
2012
Abstract
Open covering and metric regularity are properties playing a crucial role in several topics of modern variational analysis. Here their stability behaviour in the presence of perturbations is investigated in a purely metric setting. Some results in this sense are obtained, which lead to extend the known Milyutin theorem, and then to expand the concept of radius of regularity, a quantitative measure of the open covering stability. Estimations for the latter in terms of covering moduli are provided. © 2011 Springer Science+Business Media B.V.
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