The best simultaneous uniform approximation of several continuous functions on a compact set
type: Item
instance of: scholarly article
zbMATH Open document ID: 1055.41503
author: V. O. Gnatyuk
author: Yu. V. Gnatyuk
publication date: 2002-01-06T00:00:00Z
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 1685540
zbMATH Keywords: best simultaneous uniform approximation
zbMATH Keywords: continuous functions
zbMATH Keywords: compact
MaRDI profile type: Publication
title: The best simultaneous uniform approximation of several continuous functions on a compact set
published in: Kraĭovi Zadachi dlya Dyferentsial'nykh Rivnyan'
review text: Let \(C(S)\) be a vector space of continuous on the compact set \(S\) functions \(f\) with the norm \(\| f\|=\max_{s\in S}| f(s)|\), and let \(V\) be an \(n\)-dimensional subspace of \(C(S)\) generated by functions \(f_{i}\in C(S), i=1,\ldots,n\). The problem of finding \(\alpha^{*}=\inf\limits_{g\in V}\max\limits_{1\leq j\leq m}\| g-\phi_{j}\|\) for given \(\phi_{j}\in C(S), j=1,\ldots,m\) is called the problem of best simultaneous uniform approximation of functions \(\phi_{j}, j=1,\ldots,m\) by elements of \(V\). The author proves existence, uniqueness and a characterization of extremal element of the considered problem.
reviewed by: Aleksandr D. Borisenko
description: scientific article; zbMATH DE number 1685540