TY - JOUR
T1 - More on comonotone polynomial approximation
AU - Leviatan, D.
AU - Shevchuk, I. A.
PY - 2000
Y1 - 2000
N2 - The main achievement of this paper is that we show, what was to us, a surprising conclusion, namely, twice continuously differentiable functions in (0, 1) (with some regular behavior at the endpoints) which change monotonicity at least once in the interval, are approximable better by comonotone polynomials, than are such functions that are merely monotone. We obtain Jackson-type estimates for the comonotone polynomial approximation of such functions that are impossible to achieve for monotone approximation.
AB - The main achievement of this paper is that we show, what was to us, a surprising conclusion, namely, twice continuously differentiable functions in (0, 1) (with some regular behavior at the endpoints) which change monotonicity at least once in the interval, are approximable better by comonotone polynomials, than are such functions that are merely monotone. We obtain Jackson-type estimates for the comonotone polynomial approximation of such functions that are impossible to achieve for monotone approximation.
KW - Comonotone approximation by polynomials
KW - Degree of approximation
UR - http://www.scopus.com/inward/record.url?scp=0034337981&partnerID=8YFLogxK
U2 - 10.1007/s003650010003
DO - 10.1007/s003650010003
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AN - SCOPUS:0034337981
SN - 0176-4276
VL - 16
SP - 475
EP - 486
JO - Constructive Approximation
JF - Constructive Approximation
IS - 4
ER -