Approximation Properties Of Sets Research Articles

Local Approximation Properties of Sets and Continuous Selections on Them

Sets with a continuous selection from the near-best approximation operator are studied and the relationship of such sets with the radial δ-solarity property and with the metric function is discussed.

Metric Max-Distance Function in Max-Approximation Problems

The paper is concerned with approximation properties of sets in the problem of one-point approximation. The Chebyshev radius of a set is estimated depending on the behavior of the metric max-function and the diameter of the set of furthest points.

On approximation properties of sets with convex complement

On approximation properties of sets with convex complement

Approximation properties of sets with bounded complements

SynopsisGiven a Banach space X, we investigate the behaviour of the metric projection PF onto a subset F with a bounded complement.We highlight the special role of points at which d(x, F) attains a maximum. In particular, we consider the case of X as a Hilbert space: this case is related to the famous problem of the convexity of Chebyshev sets.