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Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.10 P.1451~1456

http://doi.org/10.1631/jzus.A0820015


Weighted approximation of functions with singularities by Bernstein operators


Author(s):  Bao-rong WEI, Yi ZHAO

Affiliation(s):  Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China; more

Corresponding email(s):   weibr123456@126.com, zhaoyi@hdu.edu.cn

Key Words:  Bernstein operators, Functions with singularities, Weighted approximation, Pointwise estimates


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.

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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"
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%DOI 10.1631/jzus.A0820015

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T1 - Weighted approximation of functions with singularities by Bernstein operators
A1 - Bao-rong WEI
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PB - Zhejiang University Press & Springer
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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 fCw, which extends the result of (Della Vecchia et al., 2004).

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

[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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