Shape-preserving approximation in Lp

D. Leviatan; V. Operstein

doi:10.1007/BF01208557

Shape-preserving approximation in L_p

D. Leviatan, V. Operstein

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a direct theorem for shape preserving L_p-approximation, 0<p<∞, in terms of the classical modulus of smoothness w₂(f, t_p¹). This theorem may be regarded as an extension to L_p of the well-known pointwise estimates of the Timan type and their shape-preserving variants of R. DeVore, D. Leviatan, and X. M. Yu. It leads to a characterization of monotone and convex functions in Lipschitz classes (and more general Besov spaces) in terms of their approximation by algebraic polynomials.

Original language	English
Pages (from-to)	299-319
Number of pages	21
Journal	Constructive Approximation
Volume	11
Issue number	3
DOIs	https://doi.org/10.1007/BF01208557
State	Published - Sep 1995

Keywords

AMS classification: 41A10, 41A25, 41A29
Degree of monotone approximation
Polynomial approximation in L

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KW - Polynomial approximation in L

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Shape-preserving approximation in L_p

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Keywords

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