RMC - Vol. 5, Num. 1 - Chiachio et al.

Full paper in PDF:
$%A. O. Chiachio, J. B. Prolla, and M. S. M. Roversi, Best approximants for bounded functions and the lattice operations, Rev. Mat. Univ. Complut. Madrid 5 (1992), no. 1, 39–54.%$

Best Approximants for Bounded Functions and the Lattice Operations

Ary O. CHIACHIO, J. B. PROLLA,
and Maria S. M. ROVERSI

Universidade Estadual de Campinas
IMECC, Caixa Postal 6065
13081 Campinas, S.P. — Brazil

Received: December 5, 1990

ABSTRACT

If $V$ is a closed and non-empty subset of $l oo (T)$ , the Banach space of all real-valued bounded functions on a set $T$ , then existence of best approximants from $V$ and Lipschitz continuity of the metric projection in the Hausdorff metric are proved, whenever $V$ has the following lattice operation property: $((w + e) /\ h) \/ (w - e)$ belongs to $V$ , for every $w$ and $h$ in $V$ and $e >0$ .

1991 Mathematics Subject Classification: 41A65, 41A50, 46E05.