CLC number: O174.41
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
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Bao-rong WEI, Yi ZHAO. Weighted approximation of functions with singularities by Bernstein operators[J]. Journal of Zhejiang University Science A, 2008, 9(10): 1451-1456.
@article{title="Weighted approximation of functions with singularities by Bernstein operators",
author="Bao-rong WEI, Yi ZHAO",
journal="Journal of Zhejiang University Science A",
volume="9",
number="10",
pages="1451-1456",
year="2008",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A0820015"
}
%0 Journal Article
%T Weighted approximation of functions with singularities by Bernstein operators
%A Bao-rong WEI
%A Yi ZHAO
%J Journal of Zhejiang University SCIENCE A
%V 9
%N 10
%P 1451-1456
%@ 1673-565X
%D 2008
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0820015
TY - JOUR
T1 - Weighted approximation of functions with singularities by Bernstein operators
A1 - Bao-rong WEI
A1 - Yi ZHAO
J0 - Journal of Zhejiang University Science A
VL - 9
IS - 10
SP - 1451
EP - 1456
%@ 1673-565X
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A0820015
Abstract: As an important type of polynomial approximation, approximation of functions by bernstein operators is an important topic in approximation theory and computational theory. This paper gives global and pointwise estimates for weighted approximation of functions with singularities by bernstein operators. The main results are the Jackson’s estimates of functions f∈(Ww,λ)2 and f∈Cw, which extends the result of (Della Vecchia et al., 2004).
[1] Della Vecchia, B., Mastroianni, G., Szabodos, J., 2004. Weighted approximation of functions with endpoint or inner singularities by Bernstein operators. Acta Math. Hungar., 103:19-41.
[2] Ditzian, Z., Totik, V., 1987. Moduli of Smoothness. Springer-Verlag, New York, p.56.
[3] Guo, S., Tong, H., Zhang, G., 2003. Pointwise weighted approximation by Bernstein operators. Acta Math. Hungar., 101(4):293-311.
[4] Lorentz, G.G., 1953. Bernstein Polynomials. University of Toronto Press, Toronto, p.15.
[5] Mastroianni, G., Totik, V., 1998. Jackson type inequalities for doubling and Ap weights. Rend. Circ. Mat. Palermo (II) Suppl., 52:83-99.
[6] Mastroianni, G., Totik, V., 1999. Jackson type inequalities for doubling and Ap weights II. East J. Approx., 5:101-116.
[7] Mastroianni, G., Totik, V., 2001. Best approximation and moduli of smoothness for doubling weights. J. Approx. Theory, 110(2):180-199.
[8] Yu, D.S., Zhao, D.J., 2006. Approximation of function with singularities by truncated Bernstein operators. Southeast Asian Bull. Math., 30:1169-1178.
[9] Yu, D.S., Zhou, S.P. Global and pointwise estimate for approximation by rational functions with polynomials of positive coefficients as the denominators. in press.
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