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Bernstein-Sikkema-Bézier算子的点态逼近 被引量：1

Pointwise Approximation for Bernstein-Sikkema-Bezier Operators
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摘要 讨论了Bernstein-Sikkema-Bézier算子点态逼近的等价定理,首先利用插项的的方法证明了正定理,然后应用讨论算子逼近的常规方法给出了其逼近的逆定理. We give a pointwise equivalent approximation theorem for Bernstein-Sikkema- Bezier operators, by the method of inserting term we get the direct theorem, then use the general operators method to obtain the inverse theorem.
作者 刘国芬
机构地区 河北师范大学数学与信息科学学院
出处 《数学的实践与认识》 CSCD 北大核心 2013年第1期199-204,共6页 Mathematics in Practice and Theory
基金 国家自然科学基金(10801043)
关键词 Bernstein-Sikkema-Bézier算子 光滑模 K-泛函 逼近正逆定理 Bernstein-Sikkema-Bezier operator modulus of smoothness K-functional directand inverse approximation theorems
分类号 O177 [理学—基础数学]
  • 相关文献

参考文献10

  • 1Chang G. Generalized Bernstein-Bézier polynomial[J].Journal of Computational Mathematics,1983,(04):322-327.
  • 2Ditzian Z,TotikV. "Moduli of Smoothness"[M].New York:springer-verlag,1987.
  • 3Liu Z. Approximation of continuous by the generalized Bernstein-Bézier polynomials[J].Approximation:Theory and Its Applications,1986,(02):105-130.
  • 4Zeng X. On the rate of the convergence of the generalized Szasz type operators for functions of bounded variation[J].Journal of Mathematical Analysis and Applications,1998,(226):309-325.
  • 5Zeng X,Chen W. On the rate of convergence of the generalized Durrmeyer type operators for functions of bounded variation[J].Journal of Approximation Theory,2000,(102):1-12.doi:10.1006/jath.1999.3367.
  • 6Zeng X,Piriou A. On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions[J].Journal of Approximation Theory,1998,(95):369-387.
  • 7Guo S,Qi Q and,Liu G. The central approximation theorem for Baskakov-Bézier operators[J].Journal of Approximation Theory,2007,(147):112-124.
  • 8郭顺生,刘国芬.关于Szsz-Durrmeyer-Bzier算子的点态逼近[J].工程数学学报,2008,25(1):81-89. 被引量：2
  • 9李松.Bernstein－Sikkema算子的正逆定理[J].应用数学学报,1996,19(1):144-148. 被引量：11
  • 10Guo S,Liu L,Qi Q. Pointwise estimate for linear combinations of Bernstein-Kantorovich operators[J].Journal of Mathematical Analysis and Applications,2002,(265):135-147.doi:10.1006/jmaa.2001.7700.

二级参考文献2

共引文献11

同被引文献8

  • 1Ditzian Z, Totik V. Moduli of Smoothness[M]. New York: Springer-Verlag, 1987.
  • 2Ca J D. A Generalization of the Bernstein polynomials[J]. J. Math. Anal. and Appl., 1997,209:140-146.
  • 3Chang G Z. Generalized BernsteinoB@zier polynomial[J]. J. Comput. Math., 1983,1(4):322-327.
  • 4Liu Z X. Approximation of continuous by the generalized Bernstein-B@zier polynomials[J]. Approx. Theory Appl., 1986,4(2):105-130.
  • 5Zeng X M, Piriou A. On the rate of convergence of two Bernstein-B@zier type operators for bounded variation functions[J]. J. Approx. Theory, 1998,95:369-387.
  • 6Guo S S, Qi Q L, Liu G F. The central approximation theorem for Baskakov-B@zier operators[J]. J. Approx Theory, 2007,147:112-124.
  • 7Guo S S, Liu L X, Qi Q L. Pointwise estimate for linear combinations of Bernstein- Kantorovich operators[J]. J. Math. Anal. Appl., 2002,265:135-147.
  • 8程丽.Bernstein-Kantorovich算子线性组合同时逼近的正逆定理[J].纯粹数学与应用数学,2011,27(1):56-62. 被引量：3

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数学的实践与认识
2013年 第1期

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