The degree of monotone approximation

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Publisher's DOI/URI
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Degree name
Research Report
Publisher
University of Canterbury. Dept. of Mathematics
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Volume Title
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Date
1977
Authors
Beatson, Richard Keith
Abstract

Jackson type theorems are obtained for generalized monotone approximation. Let En , k(f) be the degree of approximation of f by nth degree polynomials with kth derivative non-negative on[-~, ]. Then for each k ~ 2 there exists an absolute constant Dk' such that for all f E c[-~, ~J with kth forward difference non-negative on[-~, ~]; En,k(f ) ~ Dk W(f,n -1 ) • If in addition f' E cf-~, ~] then -1 -1 E k(f) ~ Dkn W(f!n ) • n' ' Let E* (f) be the degree of approximation n, 2 on.[ -1,1], off, by nth degree polynomials convex on the whole real line. Then there exists a constant M such that for each f convex on [-1,l] -1 E* ( f) ~ M uXf ,n ) • n, 2 The results concerning En , k are to appear in Beatson [ 1) •

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ANZSRC fields of research
Fields of Research::49 - Mathematical sciences::4901 - Applied mathematics::490101 - Approximation theory and asymptotic methods
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Copyright Richard Keith Beatson