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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Pointwise estimates for convex polynomial approximation


Author: D. Leviatan
Journal: Proc. Amer. Math. Soc. 98 (1986), 471-474
MSC: Primary 41A10; Secondary 26A51, 41A25
DOI: https://doi.org/10.1090/S0002-9939-1986-0857944-9
MathSciNet review: 857944
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Abstract: For a convex function $ f \in C[ - 1,1]$ we construct a sequence of convex polynomials $ {p_n}$ of degree not exceeding $ n$ such that $ \vert f(x) = {p_n}(x)\vert \leq C{\omega _2}(f,\sqrt {1 - {x^2}} /n), - 1 \leq x \leq 1$. If in addition $ f$ is monotone it follows that the polynomials are also monotone thus providing simultaneous monotone and convex approximation.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0857944-9
Keywords: Degree of convex polynomial approximation, Jackson-Timan-Teljakowskiĭ type estimates, moduli of smoothness, the Peetre kernel
Article copyright: © Copyright 1986 American Mathematical Society