由β - 伯恩斯坦 - 康托罗维奇型二元张量积算子进行的混合型逼近
Blending type approximation by operators of bivariate tensor product of -Bernstein-Kantorovich type.
作者信息
Cai Qing-Bo, Zhou Guorong
机构信息
1School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, China.
2School of Applied Mathematics, Xiamen University of Technology, Xiamen, China.
出版信息
J Inequal Appl. 2018;2018(1):268. doi: 10.1186/s13660-018-1862-0. Epub 2018 Oct 1.
In this paper, we introduce a family of operators of bivariate tensor product of -Bernstein-Kantorovich type. We estimate the rate of convergence of such operators for -continuous and -differentiable functions by using the mixed modulus of smoothness, establish the Voronovskaja type asymptotic formula for the bivariate -Bernstein-Kantorovich operators, as well as give some examples and their graphs to show the effect of convergence.
在本文中，我们引入了一族关于(\beta)-伯恩斯坦 - 康托罗维奇型的二元张量积算子。我们通过使用光滑性的混合模来估计此类算子对于(\beta)-连续和(\beta)-可微函数的收敛速度，建立二元(\beta)-伯恩斯坦 - 康托罗维奇算子的沃罗诺夫斯卡娅型渐近公式，并给出一些例子及其图形以展示收敛效果。
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