Convex polynomial approximation in Lp (0 < p > 1)

Ronald A. DeVore, Dany Leviatan

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that for each convex function ƒ ϵ Lp, 0 < p ≤ 1, there exists a convex algebraic polynomial Pn of degree ≤n such that [Formula presented] where ωΨ2(ƒ, t)p is the Ditzian-Totik modulus of smoothness of f(hook) in Lp, and C depends only on p. Moreover, if ƒ is also nondecreasing, then the polynomial Pn can also be taken to be nondecreasing, thus we have simultaneous monotone and convex approximation in this case.

Original languageEnglish
Pages (from-to)79-84
Number of pages6
JournalJournal of Approximation Theory
Volume75
Issue number1
DOIs
StatePublished - Oct 1993

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