Bernstein算子对具有奇性函数的加权同时逼近

虞旦盛

数学学报 ›› 2015, Vol. 58 ›› Issue (4) : 535-550.

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数学学报 ›› 2015, Vol. 58 ›› Issue (4) : 535-550. DOI: 10.12386/A2015sxxb0055
论文

Bernstein算子对具有奇性函数的加权同时逼近

    虞旦盛
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Weighted Simultaneous Approximation by Bernstein Operators for Functions with Singularities

    Dan Sheng YU
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摘要

利用在端点用Lagrange插值代替函数值的方法构造了一种新的Bernstein算子,这种新的算子可以用以逼近端点具有奇性的函数,并给出了它同时逼近的正定理.

Abstract

We construct a new type of Bernstein operators by using Lagrange interpolation to replace the values of f(x) at endpoints, which enable us to approximate the functions with singularities. The direct result of the weighted pointwise simultaneous approximation of the new operators is given.

关键词

Bernstein算子 / 加权同时逼近 / 奇性函数 / 正定理

Key words

Bernstein operators / weighted pointwise approximation / functions with singularities / direct theorem

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虞旦盛. Bernstein算子对具有奇性函数的加权同时逼近. 数学学报, 2015, 58(4): 535-550 https://doi.org/10.12386/A2015sxxb0055
Dan Sheng YU. Weighted Simultaneous Approximation by Bernstein Operators for Functions with Singularities. Acta Mathematica Sinica, Chinese Series, 2015, 58(4): 535-550 https://doi.org/10.12386/A2015sxxb0055

参考文献

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