Inclusions in general spaces: Hoelder stability, Solution schemes and Ekeland's principle

Bernd Kummer

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

49J53 Set-valued and variational analysis

49K40 Sensitivity, stability, well-posedness

Abstract
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.