文章基本信息

标题：Approximation by bivariate generalized Bernstein–Schurer operators and associated GBS operators
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作者：S. A. Mohiuddine
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-17
DOI：10.1186/s13662-020-03125-7
出版社：Hindawi Publishing Corporation
摘要：We construct the bivariate form of Bernstein–Schurer operators based on parameter α. We establish the Voronovskaja-type theorem and give an estimate of the order of approximation with the help of Peetre’s K-functional of our newly defined operators. Moreover, we define the associated generalized Boolean sum (shortly, GBS) operators and estimate the rate of convergence by means of mixed modulus of smoothness. Finally, the order of approximation for Bögel differentiable function of our GBS operators is presented.
关键词：α-Bernstein operators; Bivariate α-Bernstein–Schurer operators; GBS operators; Bögel differentiable function; Modulus of continuity