Best approximation of finite sets in normed linear spaces

摘要

In a Hilbert space, or in general, in a uniformly convex Banach space E, if K is a closed convex subset of E and a ∈ E, then there is a unique point x_0 ∈ K, called the best approximation of a in K, such that ‖a - x_0‖ = inf_(x∈K) ‖a - x‖. In this paper, we consider the more general problem when a is replaced by a finite subset A = {a_1,a_2,…,a_n} of a normed linear space E.