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Dependence of 
in Peak Norms and Best Peak Norms Approximation
Author: Yang C.
Source: Journal of Approximation Theory, Volume 104, Number 1, May 2000 , pp. 164-182(19)
Publisher: Academic Press
Abstract:
Let C[0, 1] be the space of all continuous functions defined on [0, 1] and U be an n dimensional subspace of C[0, 1]. A peak norm, or -norm for 0<
1, -norm is defined by 
f=1 sup{
A |f| d
(A)=, A
[0, 1]}, where denotes the Lebesgue measure. We say p
U is a best -norm approximant to f from U if D(f)=f-p=inf{f-u uU}. In this paper we shall study f, D(f) and P(f)={pU f-p=D(f)} as functions of for fixed f. We shall show their continuous dependence on and differentiability with respect to . Copyright 2000 Academic Press.
Keywords:
best approximation;
peak norm;
-norm;
continuity;
differentiability
Language: English
Document Type: Research article
Affiliations: Department of Mathematics, West Virginia University, Institute of Technology, Montgomery, West Virginia, 25136
Publication date: 2000-05-01
- In this: publication
- By this: publisher
- In this Subject: Mathematics and Statistics
- By this author: Yang C.
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