Stability of the operator of $ \varepsilon$-projection to the set of splines in $ C \lbrack 0,1 \rbrack $
Евгений Давидович Лившиц · Izvestiya Mathematics · 2003
We study the problem of the existence of a continuous selection for the metric projection to the set of -link piecewise-linear functions in the space . We show that there is a continuous selection if and only if or . We establish that there is a continuous -selection to () if belongs to a certain class of sets that contains, in particular, the set of algebraic rational fractions and the set of piecewise-linear functions. We construct an example showing that sometimes there is no -selection for a set of splines of degree .