Characterizations of elements of best coapproximation in normed linear spaces. (English) Zbl 0646.41025

Let E be a real or complex linear space and G a non-empty subset of E. An element \(g_ 0\in G\), is said to be an element of best coapproximation of \(x\in E\) by the elements of G if \(\| g_ 0-g\| \leq \| x- g\|\) for every \(g\in G\). Some characterization theorems for elements of best coapproximation in a normed linear space are provided. Also, characterization theorems for the specific spaces like C(Q), \(C_ E(Q)\), \(L^ 1(T,\nu)\) and \(L^{\infty}(T,\nu)\) are established separately.
Reviewer: D.N.Zarnadze


41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A50 Best approximation, Chebyshev systems