TY - JOUR

T1 - The degree of coconvex polynomial approximation

AU - Kopotun, K.

AU - Leviatan, D.

AU - Shevchuk, I. A.

PY - 1999

Y1 - 1999

N2 - Let f S ∈ C[-1,1] change its convexity finitely many times in the interval, say s times, at Ys : -1 < y1 < ⋯ < ys < 1. We estimate the degree of approximation of f by polynomials of degree n, which change convexity exactly at the points Ys. We show that provided n is sufficiently large, depending on the location of the points Ys, the rate of approximation is estimated by the third Ditzian-Totik modulus of smoothness of f multiplied by a constant C(s), which depends only on s.

AB - Let f S ∈ C[-1,1] change its convexity finitely many times in the interval, say s times, at Ys : -1 < y1 < ⋯ < ys < 1. We estimate the degree of approximation of f by polynomials of degree n, which change convexity exactly at the points Ys. We show that provided n is sufficiently large, depending on the location of the points Ys, the rate of approximation is estimated by the third Ditzian-Totik modulus of smoothness of f multiplied by a constant C(s), which depends only on s.

KW - Coconvex polynomial approximation

KW - Jackson estimates

UR - http://www.scopus.com/inward/record.url?scp=22444454016&partnerID=8YFLogxK

U2 - 10.1090/s0002-9939-99-04452-4

DO - 10.1090/s0002-9939-99-04452-4

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AN - SCOPUS:22444454016

SN - 0002-9939

VL - 127

SP - 409

EP - 415

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -