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 -