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Invariant approximation. (Polish) Zbl 0539.41038
Let A be a nonexpansive mapping acting in the normed space E and let $$M\subset E$$ be an invariant set for A. Assume $$a\in E$$ is a fixed point for A. If the restriction of A to M is compact then the set of elements of best approximation of a in M is nonempty. If M is a linear subspace of E and if A is a linear operator, then there is a fixed point of A in the set of the best approximants of a in M.
Reviewer: A.B.Németh

MSC:
 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.