Pointwise estimates for convex polynomial approximation
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- by D. Leviatan PDF
- Proc. Amer. Math. Soc. 98 (1986), 471-474 Request permission
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 $|f(x) = {p_n}(x)| \leq C{\omega _2}(f,\sqrt {1 - {x^2}} /n), - 1 \leq x \leq 1$. If in addition $f$ is monotone it follows that the polynomials are also monotone thus providing simultaneous monotone and convex approximation.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- 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