Best approximation of finite sets in normed linear spaces

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 is an element of E, then there is a unique point x(0) is an element of K, called the best approximation of a in K, such that \\alpha - x(0)\\ = inf(x is an element of 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.