Lipschitzian selections in approximation from nonconvex sets of bounded functions (Q1120769)

Let X be the space of bounded functions on a set S, endowed with uniform norm. In this paper the following problem is studied: given a (not necessarily convex) set K, find conditions on K which assure the existence of a Lipschitzian selection operator for the best approximation. Some results are stated, by using the following conditions on K: (i) if \(k\in K\) and \(c\in R\), then \(k+c\in K\); (ii) the pointwise supremum [resp.: infimum] of a set of functions on K, uniformly bounded above [resp.: below] is in K. The author indicates that other results of this kind are contained in a forthcoming paper by himself, to appear in J. Approximation Theory.