TY - JOUR
T1 - Coconvex polynomial approximation
AU - Leviatan, D.
AU - Shevchuk, I. A.
PY - 2003/3/1
Y1 - 2003/3/1
N2 - Let f ∈ ℂ[-1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials, and by piecewise polynomials, which are coconvex with it, namely, polynomials and piecewise polynomials that change their convexity exactly at the points where f does. We obtain Jackson-type estimates and summarize the positive and negative results in a truth-table as we have previously done for comonotone approximation.
AB - Let f ∈ ℂ[-1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials, and by piecewise polynomials, which are coconvex with it, namely, polynomials and piecewise polynomials that change their convexity exactly at the points where f does. We obtain Jackson-type estimates and summarize the positive and negative results in a truth-table as we have previously done for comonotone approximation.
KW - Coconvex polynomial approximation
KW - Jackson estimates
UR - http://www.scopus.com/inward/record.url?scp=0037354646&partnerID=8YFLogxK
U2 - 10.1016/S0021-9045(02)00045-X
DO - 10.1016/S0021-9045(02)00045-X
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AN - SCOPUS:0037354646
SN - 0021-9045
VL - 121
SP - 100
EP - 118
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
IS - 1
ER -