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Convex Lp approximation

โœ Scribed by B.L Chalmers; A.G Egger; G.D Taylor


Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
436 KB
Volume
37
Category
Article
ISSN
0021-9045

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๐Ÿ“œ SIMILAR VOLUMES


A Note on Convex Approximation in Lp
โœ M. Nikoltjevahedberg; V. Operstein ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 116 KB

A convex function \(f\) given on \([-1,1]\) can be approximated in \(L_{r}, 1<p<x\). by convex polynomials \(P_{n}\) of degree at most \(n\) with the accuracy \(o\left(n^{-2 i p}\right)\). This follows from the estimate \(\left\|f-P_{n}\right\|_{p} \leqslant c \cdot n^{-2 / p} \cdot \omega_{2}^{\var