Approximation of a Convex Function by Convex Algebraic Polynomials in Lp, 1 ≤ p < ∞
نویسندگان
چکیده
منابع مشابه
Convex Polynomial and Spline Approximation in Lp , 0 < p <
We prove that a convex function f 6 L p [ -1 , 1], 0 < p < cx~, can be approximated by convex polynomials with an error not exceeding Cw~ (f, 1/n)p where w~(f, .) is the Ditzian-Totik modulus of smoothness of order three of f . We are thus filling the gap between previously known estimates involving og~(f, I/n)p, and the impossibility of having such estimates involving ~o4. We also give similar...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1993
ISSN: 0021-9045
DOI: 10.1006/jath.1993.1043