Some properties of the Bézier-Kantorovich type operators
The author considers Kantorovich-Bézier type modifications of the discrete Feller operators in some classes of bounded measurable functions on an interval \(I\) (in particular, functions of bounded \(p\)th power variation on \(I\)). For such operators, estimates of the rate of pointwise convergence are given. The results generalize and extend those of \textit{X. M. Zeng} and \textit{A. Piriou} [J. Approximation Theory 95, 369--387 (1998; Zbl 0918.41016) and ibid. 104, 330--344 (2000; Zbl 0968.41011)].
scientific article; zbMATH DE number 1970540