Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity

Titelangaben

Baier, Robert ; Farkhi, Elza:
Regularity of set-valued maps and their selections through set differences. Part 1: Lipschitz continuity.
Bayreuth , 2013 . - 24 S.

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Abstract

We introduce Lipschitz continuity of set-valued maps with
respect to a given set difference. The existence of Lipschitz
selections that pass through any point of the graph of the map
and inherit its Lipschitz constant is studied. We show that the
Lipschitz property of the set-valued map with respect to the
Demyanov difference with a given constant is characterized by
the same property of its generalized Steiner selections.
For a univariate multifunction with only compact values in
$R^n$, we characterize its Lipschitz continuity
in the Hausdorff metric (with respect to the metric difference)
by the same property of its metric selections with the
same constant.