Best simultaneous approximation in Orlicz spaces
type: Item
instance of: scholarly article
title: Best simultaneous approximation in Orlicz spaces
zbMATH Open document ID: 1148.41033
DOI: 10.1155/2007/68017
author: Elsie Sterbin Gottlieb
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2008-06-03T00:00:00Z
full work available at URL: https://eudml.org/doc/54657
review text: Let \(G\) be a subset of a Banach space \((X, \| \cdot \| )\). Let \(n\) be a norm on \(\mathbb R^2\). For \((f_1,f_2) \in X^2\) and \(g\in G\) put \(\text{dist}(f_1,f_2, g) = n(\| f_1-g\| , \| f_2-g\| )\), and \(\text{dist}(f_{1},f_{2}, G) = \inf \{\text{dist}(f_1,f_2, g) : g\in G\}\). A vector \(g_0 \in G\) is a best simultaneous approximation to \((f_1,f_2)\) if \(\text{dist}(f_1,f_2, g_0)= \text{dist}(f_1,f_2, G)\). Previous papers investigated basic best-approximation properties (e.g., existence, uniqueness, characterization) for classical Banach spaces \(X\) (e.g., continuous or integrable functions on a real interval). Here \(X\) is a space of Orlicz Banach space valued integrable functions on the unit interval equipped with the Luxemburg norm. The main result is a formula for dist\((f_1,f_2, G)\).
reviewed by: Daniel Wulbert
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 5282490
zbMATH Keywords: best approximation
zbMATH Keywords: Banach space valued functions
MaRDI profile type: Publication
OpenAlex ID: W2088345170
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description: scientific article; zbMATH DE number 5282490