2011-08-11Buch DOI: 10.18452/2788
Inclusions in general spaces
Hoelder stability, Solution schemes and Ekeland's principle
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
We present two basic lemmas on exact and approximate solutions of inclusions and equations in general spaces. Its applications involve Ekeland’s principle, characterize calmness, lower semicontinuity and the Aubin property of solution sets in some Hoelder-type setting and connect these properties with certain iteration schemes of descent type. In this way, the mentioned stability properties can be directly characterized by convergence of more or less abstract solution procedures. New stability conditions will be derived, too. Our basic models are (multi-) functions on a complete metric space with images in a linear normed space.
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