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

Rao, Geetha S.; Chandrasekaran, K. R.

Pure Appl. Math. Sci. 26, 139-147 (1987).

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

MSC:

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

Keywords:

best coapproximation; characterization theorems; elements of best coapproximation