Nikolskii-type estimates for coconvex approximation of functions with one inflection point∗
نویسندگان
چکیده
For each r ∈ N we prove the Nikolskii type pointwise estimate for coconvex approximation of functions f ∈ W , the subspace of all functions f ∈ C[−1, 1], possessing an absolutely continuous (r−1)st derivative on (−1, 1) and satisfying f (r) ∈ L∞[−1, 1], that change their convexity once on [−1, 1].
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Coconvex pointwise approximation
There are two kinds of estimates of the degree of approximation of continuous functions on [−1, 1] by algebraic polynomials, Nikolskii-type pointwise estimates and Jackson-type uniform estimates, involving either ordinary moduli of smoothness, or the DitzianTotik (DT) ones, or the recent estimates involving the weighted DTmoduli of smoothness. The purpose of this paper is to complete the table ...
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