Journal of Convex Analysis 27 (2020), No. 1, 205--226
Copyright Heldermann Verlag 2020
Ioffe-Type Criteria in Extended Quasi-Metric Spaces
Radek Cibulka
NTIS and Dept. of Mathematics, Faculty of Applied Sciences, University of West Bohemia, 306 14 Pilsen, Czech Republic
cibi@kma.zcu.cz
Tomas Roubal
NTIS and Dept. of Mathematics, Faculty of Applied Sciences, University of West Bohemia, 306 14 Pilsen, Czech Republic
roubalt@ntis.zcu.cz
We study various regularity properties, including subregularity and semiregularity, of set-valued mappings acting in extended quasi-metric spaces. It turns out that this abstract framework allows to unify criteria for the usual (sub/semi) regularity as well as their directional and Hölder counterparts. Ioffe-type critera are obtained by applying a general version of the Ekeland's variational principle. We provide a self-contained material gathering and extending the existing theory on the topic. We (briefly) illustrate the importance of these criteria for applications. For example, we consider local convergence of a directional version of a Newton-type method for solving a generalized equation which may be applied when the usual (non-directional) regularity does not hold.
Keywords: Open mapping theorem, Hölder and directional metric semiregularity, Hölder and directional metric subregularity, Hölder and directional metric regularity.
MSC: 47J22, 49J53, 49K40, 90C29.
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