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有界变差函数的Durrmeyer-Bézier算子收敛阶的估计 被引量:6

Estimate on Rate of Convergence of Durrmeyer-Bézier Operaters for Functions of Bounded Variation
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摘要 在Zeng等人对有界变差函数f的Durrmeyer-Bézier算子在区间(0,1)上收敛于(1/(α+1))f(x+)+(α/(α+1))f(x-)的收敛阶进行研究的基础上,利用基函数的概率性质等方法,对其所给的Durrmeyer-B啨zier算子收敛阶估计结果作进一步的改进,得到其收敛阶的精确估计. In this paper, we study the rate of convergence of Durrmeyer-Bézier Operaters for functions of bounded variation f and obtain a accurate estimation of coefficient. Our result improves the result of Zeng by making use of probable property of basic functions.
作者 王平华
出处 《大学数学》 北大核心 2007年第1期75-78,共4页 College Mathematics
关键词 Durrmeyer-Bézier算子 有界变差函数 收敛阶 系数估计 Durrmeyer-Bézier operator bounded variation function rate of convergence estimates of coefficient
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参考文献5

  • 1ZENG Xiao-Ming and CHEN W Z. On the rate of convergence of the generalized Durrmeyer type operators for functions of bounded variation[J]. 3. Approx. Theory, 2000,102:1- 12.
  • 2Gupta V and Pant R P. Rate of convergence for the modified Szasz-Mirakyan operators on functions of bounded variation[J]. J. Math. Anal Appl , 1999,233: 476-483.
  • 3Gupta V and Arya K. On the rate of pointwise convergence of modified Baskakov type operators for functions of bounded variation[J]. Kyungpook Math. J. 1998,38 : 283- 291.
  • 4ZENG Xiao-Ming and Gupta V. Rate of convergence of Baskakov-B/rzier type operators [J]. Computers and Mathematics with Applications, 2002, 44 ( 10- 11 ) : 1445 - 1453.
  • 5GUO S. On the rate of convergence of the Durrmeyer operators for functions of bounded variation[J]. J. Approx.Theory, 1987, 51:183-192.

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