TY - JOUR
T1 - Interpolatory estimates in monotone piecewise polynomial approximation
AU - Leviatan, D.
AU - Petrova, I. L.
N1 - Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2019/2
Y1 - 2019/2
N2 - Given a monotone function f∈Cr[−1,1], r≥1, we obtain pointwise estimates for its monotone approximation by piecewise polynomials involving the second order modulus of smoothness of f(r). These estimates are interpolatory estimates, namely, the piecewise polynomials interpolate the function at the endpoints of the interval. However, they are valid only for n≥N(f,r). We also show that such estimates are in general invalid with N independent of f.
AB - Given a monotone function f∈Cr[−1,1], r≥1, we obtain pointwise estimates for its monotone approximation by piecewise polynomials involving the second order modulus of smoothness of f(r). These estimates are interpolatory estimates, namely, the piecewise polynomials interpolate the function at the endpoints of the interval. However, they are valid only for n≥N(f,r). We also show that such estimates are in general invalid with N independent of f.
KW - Degree of pointwise approximation
KW - Jackson-type interpolatory estimates
KW - Monotone approximation by piecewise polynomials
UR - http://www.scopus.com/inward/record.url?scp=85057002061&partnerID=8YFLogxK
U2 - 10.1016/j.jat.2018.10.006
DO - 10.1016/j.jat.2018.10.006
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AN - SCOPUS:85057002061
SN - 0021-9045
VL - 238
SP - 103
EP - 110
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
ER -