Approximation properties of λ-Kantorovich operators

被引:0
作者
Ana-Maria Acu
Nesibe Manav
Daniel Florin Sofonea
机构
[1] Lucian Blaga University of Sibiu,Department of Mathematics and Informatics
[2] Gazi University,Department of Mathematics, Science Faculty
来源
Journal of Inequalities and Applications | / 2018卷
关键词
Kantorovich operators; Bernstein operator; Voronovskaja theorem; Rate of convergence; 41A10; 41A25; 41A36;
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摘要
In the present paper, we study a new type of Bernstein operators depending on the parameter λ∈[−1,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lambda\in[-1,1]$\end{document}. The Kantorovich modification of these sequences of linear positive operators will be considered. A quantitative Voronovskaja type theorem by means of Ditzian–Totik modulus of smoothness is proved. Also, a Grüss–Voronovskaja type theorem for λ-Kantorovich operators is provided. Some numerical examples which show the relevance of the results are given.
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