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Some properties of the Bézier-Kantorovich type operators. (English) Zbl 1029.41009

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 X. M. Zeng and A. Piriou [J. Approximation Theory 95, 369–387 (1998; Zbl 0918.41016) and ibid. 104, 330–344 (2000; Zbl 0968.41011)].

MSC:

41A36 Approximation by positive operators
41A25 Rate of convergence, degree of approximation
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[9] Zeng, X. M.; Piriou, A., On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions, J. Approx. Theory, 95, 369-387 (1998) · Zbl 0918.41016
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